There are, believe it or not, 33 species of mosquitoes in the British Isles. Given the potential increase in global warming, and the huge increase in international travel, could tropical diseases establish here, in the decidedly untropical British Isles?
The answer is almost certainly No - there has to be a critical mass of infected people, mosquitoes capable of transmitting the disease, and fresh victims, otherwise the disease just peters out before it starts, and the UK simply doesn't have the numbers. But just to be sure, there has been quite a lot of research into the subject recently.
Historically malaria wasn't just possible in the UK, it was common. "Ague", believed now to be the vivax form of malaria, was endemic in salt marshes around England. The last recorded major outbreak of malaria was on the Isle of Sheppey in the Thames estuary , as recently as 1918.
So why no malaria now?
Well, not all mosquitoes can carry all diseases, and only 5 of the species in the UK can even carry the parasite, of which four are very rare and hardly ever bite humans anyway. The other, Anopheles atroparvus, will bite humans given half a chance, and was probably responsible for much of the Ague in the past, but it only lives on salt marshes, and it isn't even very common there. Many fewer people work on the land these days and the native strain of vivax parasite has apparently died out (no one is quite sure why) so the numbers simply aren't present. But the 1918 epidemic does give a salutary warning of what is possible.
Thousands of soldiers returning from campaigning in Macedonia were quartered in and around the salt marshes of the Isle of Sheppey. Unfortunately, many were infected with malaria and suddenly a critical mass of carriers was reached causing a mini epidemic. There were infections throughout the barracks and even 330 cases in the local population. However, a campaign of insecticide spraying and marsh draining (against the mosquito) and dosing with quinine (against the parasite) managed to bring the numbers back down, and the epidemic disappeared.
Dengue Fever is endemic in parts of South America and Asia, and so quite likely to enter the UK in infected travelers, especially as there is no vaccine. The good news is that no native vectors have been found (yet) , and the main international vector, Aedes aegypti, dies off rapidly in the wonderful British climate. Another vector, Aedes albopictus is a little hardier, but it would need quite a lot of global warming to establish.
West Nile Virus
If British mosquitoes were ever to be more than just a nuisance, this might be the reason. WNV is basically a virus of birds, and is present in many migrating birds as they pass over the UK, or stop here. That in itself would not be a problem, except one of the commonest British mosquitoes, Culex pipiens, feeds on both birds and humans, and so makes an excellent bridge. Approximately of 80% of human WNV infections are without symptoms, which is not necessarily a good thing as it allows a reservoir to build up in the population without medical intervention, and there is no vaccine. Thus a critical masses of carriers and vectors could theoretically develop.
An example of what could happen comes from the New York epidemic of 1999, where 7 people died, and there have been outbreaks in Israel and Romania. But the risk is still very low, mainly as the mosquito and virus are both relatively rare in the UK, and both prefer birds to people anyway, humans are a dead end for WMV transmission.
So, in conclusion, the consensus seems to be that there probably won't be anything to be concerned about. If you are bitten by a mosquito in the UK don't worry - just swat it and move on.
Gould EA, Higgs S, Buckley A, & Gritsun TS (2006). Potential arbovirus emergence and implications for the United Kingdom. Emerging infectious diseases, 12 (4), 549-55 PMID: 16704800
Lindsay, S., Hole, D., Hutchinson, R., Richards, S., & Willis, S. (2010). Assessing the future threat from vivax malaria in the United Kingdom using two markedly different modelling approaches Malaria Journal, 9 (1) DOI: 10.1186/1475-2875-9-70
MEDLOCK, J., SNOW, K., & LEACH, S. (2006). Possible ecology and epidemiology of medically important mosquito-borne arboviruses in Great Britain Epidemiology and Infection, 135 (03) DOI: 10.1017/S0950268806007047
For UK malaria see also an excellent site at the Wellcome Library (http://blog.wellcomelibrary.org/2012/04/item-of-the-month-april-2012-on-indigenous-malaria/)