As a former Governor of the RNLI, I can tell you that they'd be very wary of accepting Government funding because 'what can be given with one hand can be taken with the other'. i.e. under the present system, the RNLI has a fairly good estimate of what its income is likely to be for the next few years. Many Government-funded bodies (such as the Maritime and Coastguard Agency, which actually coordinates rescues at sea) have suffered massive cuts, with the possibility of more to come.
Further, if the Government starts funding charitable bodies, who is to say which other organisations should (or shouldn't) receive funding. For example, all of the UK's air ambulances are operated by charities; should they get Government-funding? If so, what about the Red Cross or hospices? There could be a very long list of bodies seeking state support at a time when all political parties agree that cutbacks are unavoidable.