Absolutely crazy to hire a car. If you stay out in Elstree your car hire + petrol, central city access fees, and parking fees will add up to overshadow the savings you're realizing by not staying in London proper. Even if you stay in Elstree, leave the car there and take the train in daily, your round-trip train costs X 2 will also be considerable.

Staying in Elstree to see London is like staying in Stamford, Connecticut to see New York. You can certainly find somewhere to stay in the city for not all that much more coin, and it will probably cost out better for you anyway given the math above.