Hmm I have the Linn Lp12 (origin live DC motor, illustrious arm, ortofon Rohmann catridge and Ear phono stage) now Naim and Linn are 'warm' sounding 'smooth' sources and the Beyer or even the Grado will do. Now £250 is a small budget if you want to get the best out of you good sources. I would say. The Musical Fidelity x-Can v3 (which also has tubes good with the vinyl) and some Grado 80's (maybe 125's if you can stretch and get off eBay) would suit you to the ground or in place of the Grado the Sennheiser HD600 are good with the Musical Fidelity so you have a good choice to start with. Note you will need to add some interconnects in the price for the Headphone Amp. By the way I saw some X-Can v3 on eBay today with about 8 days left on bidding
Anything else and your budget has to go up substantially to notice the difference. Next step would be the Senn HD650 with upgraded cable with the Graham Slee v4 'Monitor Class' (price region of £600 2nd hand

) or even the Grado RS1 with the Sugden Headmaster (price £700+

). Plus cable on top, etc.