No, not a good idea. The indigenous population of the UK should be entitled to what was promised when the NHS came about, i.e. free treatment "from the cradle to the grave."
Why should thousands of bogus asylum seekers be afforded the same rights as the rest of us? This is why the NHS is creaking at the seams because the pot's being emptied by hordes of incoming economic migrants.
Take them away, however, and the pot would runneth over yet again. The present Government has a lot of this responsibility to bear.