There’s a load. I live the other side of Newbury and I'm out most weeks.
The canal from Newbury to Hungerford is good for a leisurely ride and pub stops.
Get yourself over to Greenham common as there is good singletrack around the back of the bunkers. Its nice dry and fast at the moment. Newtown forest a little bit further out is also ace.
Also checkout snelsmore common which will be closer to you.
A lot of the rides are by local knowledge. Check out the buckled wheel bike rides that go out on Thursday’s. Their rides are medium pace I think.
A34/speed side will be ripe for checking out the myriad of byways and bridleways that head up to the ridgeway.
I'd be happy to show you around some of the local trails if you ever have need. I could name loads of areas but it all requires a bit of local know how to link it all together.