The problem is with these sorts of threads is that you'll get numerous recommendations which will all be quite different due to personal preferences. Personally, I always found the A3 and A5 MF stuff to be very warm, lacking a little in midrange insight and detail. I feel this would be more of an issue than the amp. I've never heard those particular Tannoy speakers, so I can't say whether these may be exacerbating the issue.
All you can do is audition alternatives and see which gives you what you're looking for. I'd look at the Naim Nait 5Si amplifier, Sonus Faber Venere 1.5 speakers, or trying a Chord Qute HD or Qute EX DAC to perk your CD player up a bit and ease off on its warm sounding nature.