Presumably they're required to notify everyone so I doubt they've much choice in the matter but, it might be fun to try and work it out.
There's about 7.8m people affected by the cut.
To send each a letter you'd need:
7.8m stamps (1st class at £1.35)
envelopes
7.8m envelopes (pack of 5000 for £125)
15,600 packs of 500 sheets of A4 paper (around £9 a pack on average)
3,200 ink cartridges (around £24 on average).
So, (7.8m x £1.35) + (1560 × £125) + (15,600 x £9) + (3,200 x £24) = £10,942,200 for materials.
Then you'd need to print and send them.
It takes about 0.05kWh to print an A4 letter so and average kWh costs 22.36p so:
7.8m × 0.05kWh = 390,000kWh x £0.2236 = £87,204 in electricity.
And let's say staff are paid on average £13 p/h and can process 30 letters and hour:
7.8m ÷ 30 = 260,000 hours x £13 p/h = £3,380,000 in staff costs.
That makes the total somewhere in the region of £14,409,404.
Now obviously that's based on an assumption that the government are pay average consumer prices for materials and electricity, which is unlikely, but then I've probably forgot to factor in some hidden costs so it should balance out.
So a one-off cost of £14.5m to carry out their responsibilities in terms of notifying people in order to save, according to the government anyway, £1.5bn.
Should also say maths is not my strong point so there's a good chance I've made a pig's ear of something in the above.