I think the map reference was in response to TinTin's river ride idea....
I did some of my first off road days at Richmond park, back in the early 90's.
From memory it got one or two semi-decent uphill/downhill sections, but I think they made it a bit less bike friendly for off roaders in recent years.
however, the park is beautiful and if you go at a time that isnt too busy you'll have a nice training ride doing a lap.
I used to ride a lap of the park, head out toward Ham/Kingston, and ride along the river to Hampton Court.
You can also head out of the park, head to Bushy Park in Teddington and back again.
If you want a better off road experience then you'll need to head further out.
Box Hill is great, as is Newlands Corner near Guildford.
Virginia Water makes a nice scenic ride (near Windsor, I mustve ridden hundreds of miles there) and into Windsor great Park you can do a 35 mile loop.
At the moment my favourite riding is Bracknell Forest/The Look Out, some awesome purpose built off road sections there.
But I digress....these are a fair amount further out.
Anyways, you'll give up riding once you realise there is a really good bar/pub scene in Richmond...
(but also an expensive but decently stocked bike shop.)