If you don’t mind changing the rear mech, you could open up a few more options. You could probably pick up a 10-speed SRAM X0 mech and shifters for under £100, definitely do X9 or X7 for that budget. Or a long cage 105 5700 mech which is then compatible with the usual drop bar shifters, plus the smart but spendy Ultegra flat bar shifters (R780?) and more budget Tiagra versions
If you don’t mind changing the rear mech, you could open up a few more options. You could probably pick up a 10-speed SRAM X0 mech and shifters for under £100, definitely do X9 or X7 for that budget. Or a long cage 105 5700 mech which is then compatible with the usual drop bar shifters, plus the smart but spendy Ultegra flat bar shifters (R780?) and more budget Tiagra versions