Train travel UK-Southern Spain [closed]

The Man in Seat 61 suggests that the best route is as you've described - London to Paris by Eurostar, Paris to Barcelona by TGV, then Barcelona to Malaga by AVE.

If you want to avoid Paris, you can also go via Lyon, as per Option 2 on this page, which takes the Eurostar to Lyon, then the AVE to Barcelona, or Option 3, London->Lille by Eurostar, Lille to Nimes by TGV, then Nimes to Barcelona by AVE the following day. Either way, you'd then get the AVE from Barcelona to Malaga.

There is also an overnight train from Paris to Latour, then the local train from there to Barcelona. Again see the London-Barcelona page on Seat61

To some extent your requirements are incompatible since you want to lower cost and avoid transfers. If you take the route from London to Barcelona first and then stay overnight you can work your way along the southern Spanish coast.

This map of the AVE network shows you routes where there is no AVE although I have not checked whether any of them might need a bus transfer. If you have no preferred final stop then you could make a tour of it and stop a few times on the way in Alicante or Murcia