I agree with your phasing of the easing of restrictions, but would like to differ slightly on the timings
My guess would be
Other remaining restrictions could be progressively eased in the spring, with restrictions on internal travel within the UK lifted in time for the bank holiday at the beginning of May.
- Schools and universities to return after the February half term, possibly in stages or on a part time basis until after the Easter holidays
- Non essential retail and leisure centres to re-open early March, perhaps to coincide with the budget on March 3rd, or shortly afterwards. The chancellor will need to say something to sweeten the impact of the tax rises he is going to announce, so he may announce a date for the re-opening of the hospitality sector on the day of the budget, as they do need a few weeks to prepare and order stock etc.
- Hospitality to re-open sometime between the anniversary of the first lockdown (March 23rd is a Tuesday this year) and Easter, but probably on a weekday this time rather than a Saturday. Restrictions will be similar to when the reopened last July, with no "meal only" requirement, but track & trace, table service only and 1 metre + social distancing.
- Crowds allowed back into sports stadiums from mid to late April, possibly on a limited capacity at first.
As ever, this is all speculation, or perhaps even wishful thinking, but by the beginning of March we should have a better idea of the impact of the vaccination program, and the extent to which vaccines prevent transmission as well as give immunity from the disease.
"Stay at home" needs to be in the first tranche of relaxations.