Definitely check power supply voltages. I just refurbed one of these and ALL of the Philips axial capacitors in it were dead or dying so I just shotgunned the entire thing and it's working perfectly now.
You don't need to worry about EHT voltage checks on these - entirely not needed unless the intensity pot is shot.
The 2225 service manual is freely available (google) and the voltage rails are brought out nicely onto the main board as jumper wires. There is a power supply fault isolation procedure in the manual as well if you find that rails are down.
Also the best place to post is here:
http://groups.io/g/TekScopes2Edit: you can see the jumper wires at the top left (and all the replaced capacitors):
As you're in the UK, CPC are the best place to buy cheap replacement caps. Vishay 030 are suitable replacements for the axial ones (the blue ones). I did the rest with Rubycon and EPCOS. EPCOS one is the main filter cap and had to be purchased from RS.