Compass is probably the most active moderate left of centre think tank at the moment. It's just published a paper on tax competition in Europe. This gives a feel:
We therefore propose a compulsory unified CCCTB accompanied by the introduction of a minimum tax rate. A unified basis of tax assessment combined with formula apportionment can limit the possibilities of profits and loss shifting if it is properly designed. Our proposal is that the CCCTB should be divided among member states according to a dual apportionment scheme with micro- and macro-economic components.The major part of the entire tax base should be divided between those countries where the enterprise has a base according to the micro-economic values of total wages, capital and turnover at the respective location.
In other words:
- one set of tax rules for Europe (that's the CCCTB: a common consolidated corporate tax base)
- a minimum tax rate
- and formula apportionment of profits to states.
That's the prerequisite of making a single market work. Those in the market know that. It's the theorists who don't. Unfortunately some of them are at the UK Treasury.