The drop from 0.5% to 0.25% is part of the BOE's package of measures to help the county and the confidence of the money markets since the Brexit vote. The cut, which has been rumoured to be on the cards since the referendum, means that mortgage lenders will be encouraged to pass the saving onto borrowers, reducing mortgage payments and encouraging purchases in the housing market.
The banks have reacted immediately by cutting ISA rates and savings accounts, punishing savers even further. Imagine you had a ISA account and wanted to invest £100,000 today - searching around you might do a little better but basically you would get roughly 1.2%, meaning an income of roughly £1200pa (I know compound interest will vary this slightly so bear with the rough figure). You could take the same £100,000 and buy a 1 bedroom flat and make an annual income of £6000pa - I realise you would have to pay tax of this however this is still a big difference.