In Kent:
[url=http://www.ukdirt.com/porc/]Penshurst Offroad Club[/url](probably a bit hilly)
The [url=http://www.sustrans.org.uk/default.asp?sID=1132144431328]Sustrans bike path[/url] between Tonbridge castle and Penshurst is 5 miles each way, nearly all traffic free, and has 1 hill in each direction. There are good pubs and tea shops in Penshurst to make a day(ish) trip of it.
[url=http://www.forestry.gov.uk/forestry/infd-6ljhu5]Bedgebury forest[/url] Has family trails and more interesting singletrack for when their skills improve, a bike hire shop, and a decent tea and cake shop. Parking is £5 (I think), but it all gets ploughed back into developing and maintaining the facilities.
There's also a loop around [url=http://www.bewlwater.org/]Bewl water[/url], but Marky Mark knows more than is properly healthy about the facilities and hazards there
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West of town, there is Bracknall forest with family-friendly and singletrack trails radiating out from [url=http://www.bracknell-forest.gov.uk/lookout]the Lookout[/url] centre. Parking is free, but a cycling permit is £2 per person per day. Again this goes towards maintaining the facilities. There is a cafe and bike hire place (with a small stock of spare parts) on site.