First, they have to give you quite lengthy notice and go through a consultation process for works of this size. That should buy you a little more time to raise the money. I can't remember the dates exactly but the Lease Advice website will probably have them.
Second, make sure you (perhaps in conjunction with some other leaseholders) get your own quote done for the works, from a recommended building company. It is a common scam not unknown for managing agents to use expensive building firms who overcharge the leaseholders and in return give the managing agents a kickback. If your quote is much lower, you will have a valid argument that their price is unreasonable and they should use your builder instead.
Third, you do not have to pay unreasonable charges and can go to the Leasehold Valuation Tribunal if you think their charges are unreasonable - even if you would not actually want to go to the LVT, a threat to do so often works wonders on spendthrift landlords.
Fourth, do check the scope of the works. Make sure they are only doing what needs doing and not some questionable "improvements" that may not be necessary (eg our managing agent wanted to install fluorescent tubes everywhere in our early victorian house, finally got them to agree it wasn't necessary and shouldn't be done).
On the plus side, a spruced up block will improve the value of your flat no end. If you've been there many years, do you have quite a small mortgage relative to the value of the flat, could you remortgage to cover the £20k?
merci yes they can I'm afraid.