I bought the Park tools BBT-90.3 set for about forty quid, which comes with the removal tool and a pair of cup presses for fitting. Need to add a headset press to tighten the cups, or like I did get some threaded rod and nuts & washers from the hardware store for a couple of quid…
You may be lucky if the cups just pop out, but mine have always been a tight fit and knocking them out destroys them, even though I install them with grease and use the proper removal tool.
Also be careful just using washers to press the cups in rather than the proper cup presses, as the inner bearing race is slightly raised, so all the force will go on the bearings. The proper Park tools have a raised lip which presses on the cup surround instead…