Whether the economy is strong or weak, the British government can never default on its debt. The debt is nothing more than pieces of paper that the government promises to buy back on a specific date.
During the New Deal and social democracy in Europe governments regulated capital. In the neoliberal era capital regulates government. The central purpose of neoliberal re-regulation is to remove the economic policy from control by representative democracy.
To re-enter the European Union the British government would lose its opt-out from the euro and have to adopt the Fiscal Compact. Both would be unwise and together would undermine progressive change in Britain.