I don't really know what you are up to, so it's hard to voice an opinion. But if you must have those Tannoys and have to sell your Gamut to be able to make it happen, then I would say that you will be looking at the entire preamp-amp-speakers upgrade, just not all at once. In the meantime you will need some amplification before you can afford preamp/amp to bring out the best out of the new speakers. If that's what your plans are, I might suggest selling both Gamut and Pass, get those speakers and some good integrated until your can afford separates. How about YBA Integre Passion, I saw it on sale here? It's an excellent integrated, 100 watt/ch, has XLR and RCA inputs and preamp out. Could this be an acceptable sound until better times? Or you don't expect to be able to upgrade the equipment for a long time and just want to replace the power amp with something decent?
Frankly, I have no idea how Pass works with Gamut and how Gamut works with Tannoy, maybe your speakers are fine but the signal they get is not good enough, I don't know.
My own approach is if I really like the speakers, I upgrade electronics until time comes when speakers reach their limit. In this context I upgrade speakers last. Perhaps all you need is to upgrade your Pass preamp, at least for the time being. Or cables. Or both. Again, hard to figure it out without knowing what you wish to accomplish.