EU money doesn't come out of thin air. It comes from taxpayers. The UK is a net contributor to the EU so the UK government could choose to fund all current commitments and still be better off.
For example, George Osborne has just proposed to slash the corp. tax rate from 20% to 15%, in order reduce (not eliminate) the almost certain reduction in UK investment.
Last year, CT net receipts were £ 42 billion[1]. At the current 20% rate. At 15%, that would be £ 31.5 billion, for a reduction of £ 10.5 billion. Let's divide that by 52 weeks and you get £ 200 million. Which happens to be £ 10 million more than the UK's net contribution to the EU budget.
So all your "savings" just evaporated just with corporation tax alone, and that's assuming that Osborne's plan works and there is no reduction in activity/investment, which is dubious.
[1] https://www.gov.uk/government/uploads/system/uploads/attachm...
We saw this recently in the UK when the top rate of income tax was raised to 50% and the income to the treasury actually fell.
In no way is it "almost certain" that investment in the UK will decrease. The evidence currently suggests the complete opposite. Look at the performance of the FTSE100 since the referendum to see the flood of foreign investment coming into the UK listed companies thanks to the weaker currency.
I'd also point out that decreasing tax rates is the exact opposite of what the chancellor said he would do before the referendum.
As another commenter has posted [1], this had already been debunked in December last year [2]:
This claim is based on the UK being a “net contributor” to the EU budget as a whole. The size of that net contribution varies, but according to analysis [..] about 0.6% of nominal GDP. Models of impact to the UK economy on Brexit vary. [..] even the more optimistic assessments of the UK’s economic performance following a Brexit [..] model an immediate loss in GDP for the transition years following a Brexit. The size of that loss is substantially larger than the current net contribution of the UK to the EU budget.
[Brexit] is a sure-fire short term loss, wiping any free money for R&I investment until at least a decade down the line – according to the most optimistic scenarios.
[1] https://news.ycombinator.com/item?id=12081215
[2] http://blogs.lse.ac.uk/brexitvote/2015/12/05/debunking-the-m...