Oxford walkers making for the hills often choose the Cotswolds or the Chilterns, so I was intrigued when I saw a walk entitled ‘Oxford Hills and the River Thame’ in a small book called Walking in the Thames Valley.

The guidebook’s publisher, Cicerone, made its name with climbing guides to the Lake District hills, later expanding to the Alps. It now covers many lowland areas, so its distinctive covers are known to adventurous walkers as well as mountaineers.

Oxford is, of course, in a valley, and therefore surrounded by hills, but what are the ‘Oxford hills’? Cicerone author Steve Davison’s walk turned out to feature the hilltop villages of Garsington and Cuddesdon, where some of the best views of Oxford can only be seen from footpaths.

The Sunday bus service to the start of his walk in Stadhampton is not wonderful, so we set out on a Saturday with friends, enjoying the roundabout journey on Thames Travel’s 106 service via Oxford Science Park and the Kassam Stadium (fortunately, Oxford United were playing away that day) looking forward to an adventure.

Stadhampton has a classic village green, plus a mysterious series of buildings whose origins are revealed in a two-mile historic trail designed by the Oxfordshire Buildings Trust in conjunction with Oxfordshire County Council.

Gate piers, a dovecote and building which may have been a garden gazebo represent the only remains of a manor house owned by the Dormer family. The Dormers made their fortune trading in wool but a later generation ran out of money and the house was never completed (a different branch of the family owns Rousham Park north of Woodstock).

Despite its name, the Oxford Hills walk includes a flat section across muddy ploughed fields from Marsh Baldon to Chiselhampton, which had been unpleasant to negotiate when I walked it last year.

At more than 12 miles, the Cicerone walk also seemed a bit long, so we adapted it to a nine-mile route omitting one of the villages, Little Milton, taking a more direct route to the Cuddesdon and Garsington ‘hills’.

We also decided to finish in Oxford so that we wouldn’t have to get cold waiting for a bus. In fact, our route only followed 1km of the guidebook walk, and we used it as inspiration rather than instruction.

We set off on an apparently well-used footpath leading north from Stadhampton, but failed to take proper notice of two infamous words on our Ordnance Survey map —’Stepping Stones’.

I am more cautious than my friends, so took the precaution of asking advice from an allotment holder digging his plot beside the path.

“No, you cannot get across the river Thame,” he said, telling us a story about the Queen of Denmark having blocked up the footpaths, which had never been reinstated.

Looking this up later on Wikipedia, we discovered that it was Princess Margaretha of Sweden who had lived at Chippinghurst Manor, in the direction where he pointed. But whoever was responsible for the footpath problem, it certainly has a long history. The manor is the site of an annual cricket match hosted by Victor Blank, former chairman of Lloyds, giving rise to jokes such as: ‘Trouble getting from one bank to another’.

As you can see from the photo, we decided to wade across, because the river level was low and we didn’t mind getting our feet (and thighs!) wet. But don’t do this at home, readers!

In 2006 the missing stepping stones made their way into Oxfordshire’s Rights of Way Improvement Plan. Since 2006, the county council’s countryside team has shrunk considerably, leaving volunteers from the Ramblers and other groups such as the Chiltern Society to help keep rights of way open — so for the time being, my advice is to go the long way round, across the road bridge.

You walk west from Stadhampton along the busy B40215 as far as Chiselhampton, but the consolation is that you pass an unusual church which looks like an old stable block.

St Katherine’s Georgian neo-classical clock turret is a striking sight which was honoured in verse by John Betjeman. The 250th anniversary, incidentally, will be marked with a candlelit service on December 21.

By taking the first right turn past the church entrance you can meet the Chippinghurst stepping stones site on the far side of the river and follow the path up to Cuddesdon, with views back down the Thames Valley. The village pub, the Bat and Ball, could provide a welcome respite at the top of the hill, or you could gain spiritual sustenance from the medieval church, where you can survey the rolling hills as far as Buckinghamshire.

Here we rejoined the Cicerone route briefly, taking a path west through the tiny hamlet of Denton, where the 16th-century manor house nestles in a valley formed by a tributary of the Thame.

The footpath passes a listed stable, but the house is hidden behind high walls. Walkers can get a glimpse through trompe l’oeil 17th-century Gothic windows which look as if they are part of a chapel, as indeed they once were. They are listed historic monuments, having being incorporated into the garden wall after being brought from Brasenose College, Oxford, when Victorian ‘improvements’ made them redundant.

Having decided to walk to Oxford via Shotover, we took the northernmost of several uphill paths to Garsington, which gives a good view of the Brasenose windows. From Garsington to Horspath we followed the Oxford Green Belt Way along a well walked path which is marred by a line of pylons.

The path is muddy for much of the year and we did not relish the squishy challenge, but felt it was worth getting our boots dirty to enjoy Shotover’s autumn colours. The Green Belt Way is waymarked through Horspath, and climbs to a wonderful viewpoint of Oxford’s industrial quarter and Beckley radio mast.

Here you are in urban territory, which somehow makes the countryside more precious. It was our final climb, and we were grateful for the downhill stretch into Headington, and home.

This is my final Ramblings column of the year, so I will name my top tip for walking by bus from Oxford.

As the days shorten, the 45-minute journey on the Oxford Tube to Lewknor is a joy. It is free to anyone with an older person’s bus pass and well worth the £5.90 for the rest of us.

Thanks to the Ramblers’ open access campaign and the nature reserve of Aston Rowant, there are now so many options from this bus stop, at the foot of the Chilterns, that you could do a different walk every week of the year.

Ascott Park Historical Trail map, see www.oxfordshire.gov.uk 106 bus: www.thames-travel.co.uk Oxford Tube: www.stagecoach.co.uk Aston Rowant Nature Reserve walking trails: www.naturalengland.org.uk Ramblers: www.ramblers-oxon.org.uk