Last time I had it done was at Portishead Marina but it was a few years ago now and well before Boatfolk took over.
They used a Telehandler with strops and seemed to do a competent job, allowing me to leave the masts on trestles on the hard-standing for a couple of weeks whilst the rigger and I did some work on them. I believe they now have a new Telehandler but there have been a fair few staff changes over the past year.
It wasn't cheap and I remember being slightly miffed that they charged me for lifting 2 masts (I had a ketch at the time) when the mizzen was light enough to be man-handled by the rigger.
Watchet have that enormous caterpillar tracked crane on site at all times. You could sit in the mud and have it lifted by that. No idea of price. Should be cheap but probably not.