Mosley as Prime Minister in the 1930s you say?Mosley somehow getting in the power either as a Labour, Conservative PM or some kind of less Fascist New Party probably would work for a New Deal. He was a fan of Keynesianism and probably would have been quite radical, even more so than FDR had he gotten into power.
The problem with that is how to achieve it. All the advisors at the Treasury, the Governor of the Bank of England, the experts at the Bank, the City of London, the economists, pretty much everyone except Keynes, who hadn't yet built up his reputation yet, and one other chap were all recommending that Britain go back on the gold standard. IIRC Churchill invited Keynes and the other guy to dinner and discussed the matter with them but in the end followed the weight of opinion.To improve matters Britain could abandon Gold earlier (before the Stirling crisis of 1931 forced their hand) or not gone back to it in 1925.
I can remember reading somewhere that sterling on the gold standard was overvalued something like ten or fifteen per cent, perhaps a good middle path would be to go back on to the gold standard but at ninety per cent of the pre-war level. One of the reasons that Churchill went back on to the gold standard was that he thought it would be dishonest to devalue the pound and effectively 'rob' those people who had loaned money to the government. I've got no idea if it would work economically but perhaps as part of a return to gold that sees an effective ten per cent devaluation the government offers to increase the principal of currently outstanding gilts by ten per cent or extend their maturity year so that the extra coupons pay the same as ten percent, this increase to a hundred and ten per cent meaning that investors won't lose out. The national debt increases somewhat but the hope is that a better economy will help offset it.
For underinvestment one policy could be to make money invested in new plant and machinery tax deductible, either in full or for up to a maximum of say five years. Might encourage businesses to upgrade and see some of the investment monies stay within the UK rather than going abroad.The main problems with the British economy from the 1850's onwards were structural and educational made worse by chronic under investment.