Structural problem found by surveyor - who pays?

I've gone Sale Agreed on a property that I'm really happy with. The surveyor has just been in. He said the house is great and well-built, but he identified some "minor subsidence" on the front wall of the house (there are "settlement cracks" in the wall).
To find out the cause of the problem and to figure out what will need to be done to fix it, a structural engineer will need to do some tests. We should get the surveyor's report next week and he will include estimates of the cost of the remedial work necessary. I hope to get to talk to my solicitor tomorrow as I'm not sure how to handle this.
Who should pay for the engineer's tests? I don't own the house at this stage and would expect the seller to pay. I want to make sure that the tests are carried out by a professional.
Also, if the tests reveal that the foundations need to be underpinned, I hear this is costly and would expect for either (a) the seller to pay, or (b) the cost of the work to be deducted from the sales price. Any ideas as to whether this is the usual practice?
We are paying a lot for the house (were the highest bidders by a fair few grand in a sealed bid). Obviously, we bid on the basis of a structurally sound house. We don't want to lose it.
Also, I'm not sure when/if to tell the estate agent. I suppose this is something I need to work out with the solicitor.
All advice/insights welcome.
Thanks.

Have you signed contracts and if so, were they subject to survey?

We haven't signed contracts yet. We are due to sign next week. When we went Sale Agreed, it was subject to survey.
We still want to buy the house, just don't want to be stung for the cost of fixing the problem.
Thanks.

You can always ask the sellers to cover the costs, but I can't see how you could insist - Are you prepared to walk away from the deal if they refuse?

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I have often heard in this scenario that the sellers will get the work done and claim it off their insurance if it is covered before then signing the house to you. usually then you would get a cert to say the work was completed...

Re: ..

There is no obligation whatsoever for the vendor to fund structural analysis and there is no question of the vendor being liable for the cost of structural repair. "Sale agreed, subject to contract", imposes no obligation on either party. It is completely unenforceable in law.
Should the vendor choose to engage with you and process a claim through house insurance, I'd consider yourself very lucky. I expect that the vendor will simply go back to an underbidder unless you can come to some mutually acceptable reduction in price.

Re: Structural problem found by surveyor - who pays?..

You approach the seller and ask for a drop in price consistent to what you have been quoted by professionals to fix it. They may say forget it, and hope to sell to somebody who doesn't take the time or cop on to get an engineers report. Or they may feel caught out and want a quick sale and say ok. It's up to you ultimately. They are either ignorant of it or just trying their luck, but ultimately they don't have to fix it.