I'd guess you'll actually be wandering down the east coast to West Sussex, but just in case you are heading down the west side of Britain, one of the most ancient bits of forest has recently been revealed on the west coast of Wales, at Borth in Cardigan Bay, where winter storms swept away sand and underlying peat at the coast, revealing the remains of 5,000 - 6,000 year old oaks, alder & birch.
Further south west, Dartmoor has a number of areas of truly ancient oak forest, Black'a'tor copse & Wistman's Wood.
This will be quite a bit out of your way if you're heading for Sussex