Norman correctly states that Marble Arch station serves Hyde Park. (It's opposite Speaker's Corner). However, I'm guessing that you might be going to Hyde Park for a gig. (O2 Festival? Peter Gabriel? Aerosmith?). The entrance for concert-goers is the Queen Elizabeth gate, which is served by Hyde Park Corner tube station, on the Piccadilly Line.
The simplest way to access the Piccadilly Line would probably be to park at Cockfosters. Take the M11 to the M25 junction. Join the M25 anticlockwise. Continue for 3 junctions. Leave at Jn 24, taking the 2nd exit at the roundabout, onto the A111. Cockfosters tube station is 2� miles along, on the left. The car park has 460 spaces.
I'm not sure what is meant by the suggestion that you could park at Epping Forest. The forest itself is 4� miles long and 2 miles wide. No part of it is close to any tube station. However, parking at Epping station might be an option. (It will save you about 15 miles driving, when compared to Cockfosters). Leave the M11 at Jn 7. Follow the B1393 into the centre of Epping (which is about 3 miles from the motorway). Look for a turning on your left (Station Road), signposted for the station. There are 525 parking spaces.
Epping is served by the Central Line and, as Norman indicates, you could simply travel straight through to Marble Arch and walk from there. However, for easier access to the Queen Elizabeth gate, it wouldmake sense to alight at Holborn and then follow the signs taking you to the westbound Piccadilliy LIne (for Hyde Park Corner).
Both Cockfosters and Epping station car parks are very busy; you might find it difficult (or impossible) to find a space. A day return ticket, by rail from Cambridge to Kings Cross, costs �18. (The last train back departs just after midnight, so you wouldn't have any problems getting back after a gig). Kings Cross is directly linked to Hyde Park Corner, by the Piccadilly