You might want to build it on tor network.
Not going to happen.
I'm one of the parties involved in discussions. Nothing is actually agreed yet - and certainly nothing would be agreed by me personally unless a bunch of different elements line up. One of those elements being that the exchange can legally operate in the UK.
Broadly speaking there are three legal obstacles which have to be addressed:
1. That holding BTC on behalf of investors/users and transferring it to other users doesn't subject the operators to financial supervision OR to a need to obtain AML/KYC details from users. This one we're already basically certain we're fine on - due to legal advice received and precedent already set.
2. Whether, regardless of BTC being used, the 'securities' themselves are illegal and/or subject to regulation. This is the key one - but there IS a very interesting case to be made that they're fine because of the way HMRC treat Bitcoins. Legal advice is currently being sought on this.
3. That having US investors (with the rules in the US being VERY different) is OK. This one is interesting - but the answer is almost certainly that a UK-based exchange could NOT accept US-based investors as - even if fine to operate in the UK, it would break agreements between the UK and the US. So there's a very real likelihood that any new exchange would not take US investors - the situation with US companies is less clear.
For those confused how the situation could possibly be so different in the UK to the US, the answer lies in their totally different approach to treating Bitcoins.
The US is moving very much towards them being treated as though they were (similar to) currency for the purpose of regulation.
The UK, in contrast, is saying that they have no face or intrinsic value and thus can't be referred to in accounts and aren't subject to regulation. They're explicit, in particular, that any conversion from BTC to fiat has to be treated as income tax (for individuals) and revenue (for companies) and can never be claimed as capital gains or investment return. This actually has very BAD consequences for businesses raising funds in BTC then converting them to fiat to (for example) buy mining hardware - but has very GOOD consequences for those looking to run something like an exchange.
I'm not going to lay out the argument that follows from this - but I believe there IS a strong one and am personally obtaining advice on it in the next week or so (even if I don't end up participating in an exchange it would be very useful information in respect of any BTC securities I operate).
So no - Tor isn't on the table (not as far as I'm concerned - and noone else involved in the discussions has expressed an interest in it). All of those talking want something openly run in a jurisdiction where there's no likelihood of interference from the authorities - and the UK might be that place.
I believe the OP was made prematurely - and the title is misleading. As MPOE-PR pointed out, there's no plan yet - though the intentions aren't actually entirely vague (just not detailed in the OP). And noone should read this as BTC-TC coming back with all securities and user-accounts etc - if burnside's code is purchased it's certain the data won't come and that it would be rebranded. Burnside's code is NOT the only option under consideration - but it would be far preferable to a newly written system because of already having been heavily tested in a live environment.
Don't expect updates from me in the near future - but I felt I should at least confirm that when Kate says various issuers/others are involved then it definitely is the case : and statements of available investment have been made, though not committed to (i.e. I and others have said "I have X BTC I'd consider using for this" not "I have X BTX that is definitely going to be used for this").