This is from the Evening Standard ...
"the Department of Health and Social Care (DHSC) received a 10 to 15 per cent discount from BCG, whose day rates for public sector work range from £2,400 to £7,360 for the most senior consultants."
The day rate is what BCG invoice DHSC for providing consultacy services. Those figures might include VAT, I can't see for certain if they do or don't and the Sun say it is before the discount is applied. It's likely that the top rate will be rarely charged.
When running a consultancy business you have other costs to cover. Training, office space and equipment, back office support staff, hotels, travel, software costs and licences, insurance, pensions, sick pay, bench time* (when staff aren't earning or training like when a player is on the bench in football he still gets paid, it's the same with consultants.) After that you need to try to make a profit otherwise why bother.
There is (I'm pretty sure) no-one getting paid £7k+ per day.
Politicians and journalists quoting this figure and stating that this amount is being paid to people in an effort to discredit them only goes to show how thick they are in understanding how business actually works. The rates are what they are due to market forces. And yes, it is unfair that an IT person gets paid £100k pa but a nurse gets paid a third of it. Knocking wages down to parity doesn't fix that, the talent pool is already small, hence the rates, so would only reduce it further.
www.lbc.co.uk