We often stay in villas and never had to pay that much, especially for a week, even in school holidays.
However, some weeks are dearer than others, and it depends on your location.
We have recently booked a lovely looking 4 bed villa in Playa Blanca, with a heated private pool and jacuzzi, for a week in Easter holidays for £1350 in total. From mid July for the summer is goes up to £1800
Had a fantastic villa in May holidays last year, in Majorca - that was a really fabulous 5 bed, again with private pool and jacuzzi. That was a bit dearer as 5 bed at 2500 in total for the week. However, this one is much dearer to go to in July/August - would be £4000+ - It is cheaper in June, but goes up on 1 July.
Are you clear on what you want: where, amenities, distance to beach, car or not, pool, etc
5 bed is harder to find than 4 bed and will therefore both restrict your choice and increase the cost - you sure you can't manage to fit the 8 over 4 rooms instead?
We use holiday lettings.co.uk or home away.co.uk