If you’re happy playing in the mud off road, or for future reference, then there’s good foresty singlestrack riding from the doorstep in Reading. Map link for starting points here: Streetmap linky
Lots of singletrack in the woodland sections between Mapledurham, Woodcote, Checkendon, some cheeky, some bridleway. The Thames Path from Whitchurch to Goring is a swoopy blast. For hillier off road stuff scroll a bit further North to the area around, and to the north of Nettlebed. Hours and hours and hours of fun.
Whenever I look at those maps I realise we’re fairly well provided for here. But yep, Swinley might be the best bet for you