This morning the tap on the bathroom basin decided not to turn off.It has a lever action. I turned it off by the isolation valves on the pipes.
Can anyone tell me if it is something I could fix or should I get someone in?
My personal opinion is that the tap itself is unlikely to be repairable as such but it is not a major job to replace it or a part of it with the right tools - you are presumably a good judge of whether you can or not. Is it a mixer tap or are there separate hot and cold ones, one of which has failed ? This is an example of what can be done in the case of single source (non-mixer) taps, just make sure your lever has the matching number of splines.
https://www.ebay.co.uk/itm/Basin-Lever-Tap-Replacement-Heads-Handle-Conversion-Kit-H-C-Pair-1-4-Turn-TCK3/171562960879
Mexican same difference, just measure between centres of hot and cold feeds, think they are standard, but not totally sure then take your pick. Take it you have flexible connectors supply to tap?