Depends how you define progressive. If we view it simply in terms of income tax, then we have a system that you could argue is very progressive and weighted in favour of low and middle earners - even in comparison to Germany (which is itself quite progressive when compared to other EU nations):
UK income tax
£0 £11,500 0%
£11,500 £45,000 20%
£45,000 £150,000 40%
£150,000 - 45%
Germany
€0 €8,354 0%
€8,355 €13,469 14% − 23.97%
€13,470 €52,881 23.97% − 42%
€52,882 €250,730 42%
€250,731 - 45%
I have lived in an EU country (under a socialist government) where both the tax and welfare systems were decidedly less 'progressive' and where austerity measures cut deeper than anything we experienced in the UK.
You say the Labour manifesto is 'fully costed', but that costing doesn't stand up to any sort of scrutiny. The fact they are proposing up to one quarter of a trillion pounds in additional borrowing has to raise alarm bells.
You can pick holes in the record of the Tories in government. There is no escaping the fact that they inherited a mess. Since then we have seen sustained growth, falling unemployment and a reducing deficit. They may have missed their targets in a number of areas, but show me a government that hasn't.