Space in central London is at a premium and is in high demand. Hence, expensive prices.

The question is where will they be over the 8 days. If you are all flying, then leaving all cars at the airport long term car park is likely to be the cheapest option.

If you are after cheap long term parking then, looking at the airport long term parking and taking the shuttle to the airport and then the tube/train to central London is another option. For Kings Cross, consider Luton airport area with a direct train link into Kings Cross

Another consideration is to look for safe road side parking further out of town and take a taxi to the Kings Cross area.

There is free road-side parking along side Euston from Friday evening to Monday early morning but eight days is pushing it.