We get a reasonable number of people wanting to change from ss to valve, and a decent integrated seems like the ideal first step to make. The only problem is that the preamp part of a £2k-£3k integrated is not particularly brilliant, ie you get a flavour of valves, but not the whole story. We used to sell Conrad Johnson, who made a brilliant integrated, the CAV 50. It was not the most powerful amp, but partnered with a pair of sensitive Triangles or J M Labs it was sublime. Audio Research still do a similar beast, but with more grunt and a slightly more forward sound than the CJ, but it lacks the posh fascia and lovely knobs that have adorned their integrateds in the past, (also called the CAV 50 I think). Both of these products are good, but being premium brands command premium prices. In the case of the CJ they are unavailable and rarely come up s/hand.
Outside of these two brands, there is BAT, but not sure if there is an importer. The good thing about CJ and ARC is that there is excellent service if you look around and parts are readily available. Outside of these, and leaving aside the myriad of Chinese built stuff, Rogue Audio is excellent. Never had a problem with it from a reliability point of view, and it sounds great. Due to certain reasons, you may have to look hard for a retailer where you can go and hear the stuff, but it is worth it. It had great initial reviews and was very cheap for what it offered. Having met Mark O`Brian, one of the founders, his enthusiasm for good gear at lowish prices means that, even with an importer`s mark up, it still offers good vfm. It is also load tolerant and may have a stab at driving your Kef`s, but I feel you would be best to change your loudspeakers. Or buy a pre-power instead.
The alternative would be to look at Prima Luna. These amps are bullet proof, ultra reliable and powerful especially the pre and power combinations. The Prologue Five power amp will give you plenty of current. We put Genalex KT88`s in ours and it sounds excellent. You really need to get out there and try a few. You should find it a really enjoyable experience and your cd`s will benefit from the warmth and richness that a good valve amp can bring.