Until the past year or so, the conventional wisdom was that blight can only survive on living plant tissue. so it was considered safe to compost blight-affected plants remains.
The situation in the UK is not quite as certain now, according to the RHS:
The presence of new blight strains in the UK means that the pathogen now has the potential to produce resting spores (oospores) in the affected plant tissues. The oospores are released from the rotting tissues to contaminate the soil. These resting spores have yet to be found in the UK, but analysis of the recent variations occurring in blight strains in some parts of the UK suggests that they could be being produced. Little is currently known about their survival and their potential as a source of the disease, but investigations are continuing and more information is likely to become available over the next few years. However, because oospores are resilient structures, if they are produced in infected foliage it is quite possible that they will survive many home garden composting systems. This is why it is preferable to dispose of waste from blighted crops in other ways. Municipal and commercial composting systems reach the very high temperatures necessary to kill oospores and other resilient pathogen propagules.
(Full article:
https://www.rhs.org.uk/advice/profile?pid=217)
The risk of blight persisting in your soil, either outside or inside is therefore still very low at the moment - the main precaution I take is to bin rather than compost the remains of my tomatoes and potatoes.