If I have understood your post correctly, you are saying that you have had too much income assessed (and therefore taxed at an unnecessarily high rate) because there were delays in bringing your pension 'online' and it was physically paid to you (or started to be paid) some months after the commencement of your claim.
This is distinct from your decision to defer your pension: if the deferral resulted in higher annual pension income and more tax, that is an unavoidable consequence of your decision to defer.
It may be that things will work themselves out over the course of the tax year: monthly pension may have been taxed too highly on the initial "lump" but pension income is ultimately taxed by reference to cumulative income received over the tax year as a whole. This could result in your getting a tax refund automatically, but after the end of the tax year when "End of Year Reconciliations" are run.
But it could mean that your total income for the 2020/21 tax year overall takes you into a higher tax band and some of it will now be taxed at a higher rate, and some of the income that 'belongs' to 2019/20 would have been taxed at a lower rate (or not at all) if it had actually been paid to you through PAYE in that earlier year.
A registered pension scheme (most pension schemes are registered pension schemes) is taxable as it accrues, not as it is paid. This is in accordance with ITEPA 2003 s 571 and s 579B, et seq.
HMRC's manuals confirm this in the employment manual at EIM74101, and the Self Assessment Manual at SAM20030:
"In many cases, the taxable pension income for a tax year is the amount accruing in that year irrespective of when any amount is actually paid. Where accruals basis applies, the pension, etc. should be assessed on the amounts that the pensioner is entitled to in the tax year
Pensioners are often content to pay income tax on the amount received in a year, as, in most years the amounts accruing and received are similar. However, it is possible in certain circumstances for the amounts to be different. If a taxpayer requests the statutory basis this should be accepted." (Extract, see EIM74101 as per the above link for more - and check how your particular category of pension income is taxed on the table therein)
I don't know whether you are in Self Assessment or not but the guidance on those pages explain the principles and the steps HMRC should take. You will end up with a liability in 2019/20, for pension income to which you were entitled but did not receive. If you have done your sums correctly, (and assuming I have understood your query correctly), then your 2020/21 tax overpayment should be larger than your 2019/20 underpayment, resulting in a net tax repayment.
I trust this is useful.