She said she was working on possible limits to free movement with other EU nations - a "growing number" of whom were concerned about "sham marriages" and other abuses of the system.
BBC: UK will not extend Romania and Bulgaria migration curbs
Admissions body Ucas said the number of non-EU applicants had risen 24.7%, with applications from the EU going up 6%.
But that will depend on persuading all EU countries to share passenger and crew list information - quite a number of them regard this as illegal under European free movement laws.
The number of visas issued to skilled non-EU migrants without job offers - known as tier 1 - would be cut by 13, 000 to 1, 000, and the corresponding number of visas issued to those with job offers - known as tier 2 - would increase by 7, 000 to 20, 700, Mrs May explained.
Migration Watch's chairman cites events from 2004, when the government grossly under-estimated the number of migrants that would travel from new EU states such as Poland.
Meanwhile there are a number of local battles with smaller parties like the Greens and the anti-EU UK Independence Party fighting hard to capitalise on disillusion with the big three parties.
The Rock has become a tax haven, which a good number of Spaniards benefit from, and needs far-reaching reform, according to both the EU and the OECD.
Since 2004, when many large Eastern European countries joined the EU, more than one million people from those countries have come to live and work in the UK - a huge number.
Then on Wednesday, Switzerland, not a member of the EU but part of its passport-free travel zone, invoked a special safeguard clause that allows it to cap the number of workers from 28 European countries.
Hightlights include a double-headed session of the Home Affairs Committee on drugs and extradition (at 11am) and another double-header from the Transport Committee starting at 9.35am with evidence on whether new EU proposals to regulate the number of hours that pilots fly will compromise aviation safety.
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