Membrane, where installed in association with suitable drainage.. yes this means channels and pumps(!) if correctly designed and installed will provide protection against groundwater pressure coming to bear, meaning that in the event any unforeseen circumstance i.e. burst water main etc. the internal environment would be protected.
This type of waterproofing is lower risk than cementitious tanking because you are not reliant on forming a 100% perfect barrier to water, it can be tested by introducing water into the system, (whereas you can't really flood the ground external of the structure), it will tolerate movement in the structure (rigid tanking won't), is not reliable on the condition of the substrate to which it is applied, is more tolerant of post installation damage so if you sell the property and someone hangs a picture they probably aren't going to affect the waterproofing, whereas a nail in a 'tank'... I could go on but for these reasons, 'drained protection' waterproofing is recognised within British Standard 8102 Protection of Structures Against Water from the Ground, as 'being the most effective and trouble free'.
If you're choosing between tanking and drained protection, go with drained protection.
If you're talking about membrane in isolation (no channels/pumps), this will simply isolate internal finishes from potentially damp walls. This is dampproofing, not waterproofing, and if water pressure should come to bear, it will penetrate into the internal living environment.
In respect of breezeblocks, the use of blockwork is common below ground and these would not be affected by groundwater save for perhaps in the event of agressive groundwater conditions (sulphates) which could affect the mortar, but to be honest I would not worry.
If there is an inner leaf of block, this has either been put up to support a suspended timber floor over (possibly rotten joist ends bearing into damp externals), or is there to aesthetically cover what may otherwise be a damp wall. Personally, subject to it not being structural
, I would look at taking it down and gaining back some living space.
Thanks for your offer to quote and we do work nationwide but we are a fairly large firm with overheads i.e. Professional Indemnity Insured design etc. (same insurance your Architect/Engineer carries) which our smaller man and a van competitors never carry and I can guarantee we would come in a fair bit more expensive than the quotes you have already received. Still, If you are interested and wanted indicative costs, PM me your email and i'll send you some further info. I do know a reputable company in the Midlands who may assist.
One other brief comment, use an established firm where the guarantee is actually worth something, and ideally get GPI guarantee insurance (FSA regulated insurance co.) so that if they cease trading and you have a problem, it's covered and you don't have to pay out again. You have no idea of the amount of companies which start up, do poor work and then go bump, leaving all involved totally in the lurch
Mike, presumably this is newbuild? Much of the failed work that we do address is associated with externally applied tanking systems, and commonly the issues are associated with incorrect land drainage. I've been speaking with an Architect in Notts today on an external tanking scheme with issues, and am at a £3.25m house in manchester with issues next week which I think is also externally tanked.