The letter from Mrs May to Nick Clegg, which has been seen by The Sunday Telegraph, proposes a tough new minimum income of £25,700 a year for anyone seeking to bring a spouse, partner or dependant to the UK from outside the European Union from June – almost double the current threshold of £13,700.
The minimum income would rise dramatically – up to £62,600 – if children are also brought in.
Mrs May also wants a longer probationary period of five years before spouses and partners can apply to live permanently in Britain, and a higher level of English to be required.
The proposals could cut the number of immigrants allowed in by 15,000 a year – a significant step towards the Government’s aim of reducing “net” migration to 100,000 people each year.
However, they are expected to fought hard by Mr Clegg and other Liberal Democrat ministers, escalating still further the tensions between the two Coalition partners that have risen dramatically since last week’s controversial Budget.