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Both. Migration from countries with high HIV infection rates is clearly an important factor, but there are many other factors at work. About half of British Africans who have been diagnosed with HIV became infected while living in the UK. British-born Africans are at a lower risk of HIV infection than immigrants, but they're still a high-risk group.
The majority (67%) of British Africans are first-generation immigrants, infection rates differ widely across African nations (19% in South Africa vs 0.7% in Somalia) and different immigrant groups have differing patterns of settlement in the UK and sexual behaviour, so it's very difficult to predict future trends in HIV infection rates amongst British Africans. Demographic shifts could cause a very rapid increase in new infections.
The restriction applies to people who have recently been sexually active in Africa, but not to people who have been sexually active with Africans. The latter represents a very significant route for new infections, but is not acknowledged by the Blood Service.
It's an educated estimate. There are various methods, but the most common uses antibody testing on recently diagnosed patients to get a rough idea of how recently they were infected. This can then be extrapolated out to cover a whole demographic. That estimate can be fine-tuned by looking at historical trends, as everyone who becomes HIV positive will eventually either get diagnosed through testing or develop an AIDS-defining illness.