How confident are you with spreadsheets? Only you know your personal circumstances (finance, lifestyle etc) so only you will know if you are ready to retire or need to continue working.
In my own preparations (I’m 56 and hoping to retire at 60) I started with a budget, working out what my regular expenses are now and what would be the amount I needed to cover these. What are the fixed items (e.g. Council Tax, Utilities, Rent?, Telephone, TV (Licence, Cable/Satellite service), Car etc)? What are variable necessary expenses (Groceries, Maintenance, Public Transport expenses etc)? Once these are covered then think about discretionary spend such as hobbies, holidays, leisure etc.
Once you know what your expenses are (this is where the spreadsheet comes in) note them down and work out your totals. Think about what savings you have (if any) and any other investments (e.g Stocks and Shares ISA). This may be alien to some people.
My biggest resource has been YouTube. There are some excellent videos by Pete Matthew under MeaningfulMoney, and Chris Bourne. They are both Independent Financial planners in the UK so all details are relevant. They suggest starting with a budget and calculating your expenses & also making sure you have paid your debts off before (or at retirement).
There is a lot to cover, but if you are confident in your own calculations you do not need to use an Independent Financial Adviser (their fees can be quite high, I’ve found).
I am assuming your public sector pension is a defined benefit (final salary) scheme which are the gold standard in pensions. Unless there are restrictions with your other pension, I would have thought you can claim this at any time (e.g. now). Many pensions schemes indicate an “intended” retirement date (e.g. 65) but that is usually just the expectation with the pension provider who, if you are on a default scheme, will usually start changing the way your pension is invested as you approach the intended retirement age
Whatever you do I wish you all the best