William Lewis at Orchid vet in Brentwood is the local exotics expert so would be the best bet if that's near
Lawton in Harold Hill is another exotics expert
South Beech in Wickford is supposed to be an exotics specialist who take bunny referrals, but I don't have personal experience
My own vet at Vets4pets Braintree is very bunny savvy
Simone at Companion Care Chelmsford isn't too bad if they are fairly central (but I think the others on this list are probably better if they are get-to-able)
Essex is a big county so it really depends whereabouts they are and how far they are prepared to travel/how much they are prepared to pay.