We've been quoted to lay our patio straight onto sand, but will it last without a proper base?

No, I wouldn't sign that one off as it stands. Sand on its own shifts as the ground beneath it settles and as rain washes it about, so within a season or two you tend to get slabs that rock, lift at the edges and trap water in the joints. It can look spot-on the day it's finished and be a mess by the following winter.
What a patio actually needs underneath is a compacted sub-base, 100 to 150mm of MOT Type 1 hardcore whacked down with a plate compactor, and then the slabs bedded on a full mortar bed rather than five dabs under each corner. That dot-and-dab shortcut leaves hollow voids that crack the slab the first time something heavy lands on it. The surface also wants to fall away from the house by roughly 15mm per metre so rainwater runs off instead of pooling against your wall.
The one time sand is the right call is block paving, where the blocks sit on sharp sand over a proper base and lock together. That's a different job from laying slabs.
When you compare quotes, get each firm to put the sub-base depth and bedding method in writing, and ask what fall they're building in. A price that looks cheap usually is, because the groundwork is exactly where corners get cut and you can't see it once the slabs are down. As a rough guide a properly built slab patio runs about £90 to £180 per square metre all in, more for porcelain or an awkward site. There's a full breakdown of what a patio costs here. If you'd like a few firms who'll quote to that spec, we can match you with vetted local builders for free.