According to this page, any deferred lump sum amount is fully taxable, so he should aim to minimise the marginal tax bracket it will fall into. With PAYE of £31.4K and the annuity of £2k, and a higher-rate tax threshold of £9.4K+£32K = £41.4K for 2013-2014, that leaves about £8K to play with in the 20% band for 2013-2014.
If he's got about 16 months worth of deferred pension (state pension age of 65) then that would be £10-11K so he'd end up paying a bit of 40% tax.
For future years after retirement the income would be roughly £2K+£8K which pushes him into or very close to the 20% band given the personal allowance will be £10K or £10.5K. So it'll be hard to avoid paying 20% tax but 40% should be easy to avoid.
Alternatively if the lump sum is not needed, opt for the enhanced pension - you get a 1% uplift for every 5 weeks of deferral and given the likely trajectory of the personal allowance etc the extra would probably escape going above it.
I don't think the pension changes in the recent Budget (March 2014) make any difference to any of this as his private annuity is apparently already in payment. I haven't heard any suggestion that the lump sum for deferring the state pension can be treated as part of a normal private pension pot.