In your shoes (with any relatively inefficient speaker, actually), I always choose a used amplifier so that I can get better quality and power for less money. I don't own the Elac speakers, but I have read that they need power, and that's not uncommon with small speakers. Henry Kloss wrote an article nearly 40 years ago (Hofmann's Iron Law) that made that case in the context of acoustic suspension speakers, but it's true for ported dynamic speakers as well--the smaller the volume, the less the efficiency.
I run an older Adcom GFP535 with Pioneer SP-BS22LR speakers, which are similarly small (actually, smaller) bookshelf speakers. I think I paid about a hundred dollars for it a couple of years ago. That amp is rated at 60 watts, but has an abundance of headroom, and it achieves comfortably loud levels without strain at all (other than having a ported speaker boominess in the mid-bass). It rolls off in the deep bass, but that's not from lack of power. I seriously doubt anyone will hear the difference between that amp and those that currently measure at the top of the heap, especially at lower levels.
But you can also get something newer and that measures pretty well even by today's standards. I'm using a pair of B&K Reference 125.2 amps to drive a pair of Advent loudspeakers, which are also rather inefficient (but which have far deeper bass). I paid at most $300 for each of them. They were made about 15 years ago and are still in excellent condition. They truly are the next step up in power from your Audiolab at 125 watts per channel.
Of course, both of these are power amps, which you would feed from the pre-amp outputs on your Audiolab.
And granted, I'm giving USA prices for USA-made stuff, but I'm assuming the UK price penalty will still allow you to buy something similar for much less than your budget.
All that said, I'm doubting a new amp or bigger amp will change your life in your use case. But I'm betting a sub-woofer will. So, my real recommendation is to spend your budget on two good powered subwoofers (they needn't be particularly large or powerful), which you can also feed from your pre-amp outputs. I'm one who prefers two subwoofers for stereo music listening, even if it's not supposed to matter much, but it resolves the issue of not having a subwoofer output on your amp that blends both channels (unless your amp has a feature for doing that with one of the preamp outs--check to see).
Rick "uses a sub for home theater but generally prefers not to for stereo music, especially with speakers that are already good down to 30 Hz" Denney