Fox Umbrellas in London EC2 ( I think) are reputed to be the best, - a long-established firm, but expensive - on the other hand, if it is a lovely thing it may be worth it : they will restore/service the frame as part of the process.
Be careful about having a go yourself, or getting anyone who doesn't specialise to do it for you : the fabric needs to be under quite a bit of tension, and if the frame hasn't worked properly or even been used for a while the unaccustomed strain can be too much for the spokes. I speak as someone who completely buggered a lovely Edwardian parasol once.
Vx
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Viva la Belvoir
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