The UK has always been warm enough for malaria, and native mosquitoes are quite capable of carrying it. Our endemic malaria, ague, was once widespread in the Fens.
The microbe that caused it, Plasmodium, was discovered in the 1890s, just as drainage of mosquito breeding sites was diluting the disease to the point of extinction.
However, soldiers returning from World War 1 brought malaria to repatriation camps in Kent, where local mosquitoes picked it up, resulting in 491 cases. The outbreak was contained, with a repeat after World War II.
Ague was the mild P. vivax (mortality 1–2 per cent of untreated cases); the more deadly P. falciparum (25–50 per cent) needs tropical heat.
Even the worst warming scenario is unlikely to change our climate sufficiently; the story in Southern Europe, the USA, Central Asia and Australia could be very different.