Thank you for your previous rating. I will try to reply to your question as clearly as possible, bearing in mind that the area you inquire of now is not governed by written law but by unequally applied precedents.
First of all, there has been no legally binding result as an effect of implied conduct during negotiations, unless you signed throughout "intermediate agreements" (i.e. agreements to maintain the provisions which had been agreed to up to that point), which is very unusual.
The most that could be obtained in your situation would be damages. These damages would not be in lieu of the execution of the contract, but for violating an obligation of negotiating in good faith if such can be deemed to exist.
As a principle, this obligation does not exist under English law, but there are many exceptions. I will enumerate and explain those which may be applicable to your case:
1. Lock-out agreements, if the other party suffered damages as a result of being locked-out of negotiations with someone else;
2. Agreements to use "best endeavors" or to achieve fair price or cost. The "best endeavors" clause should be interpreted widely. In other words, a lot depends on the wording of the LOI. If there is some sort of deadline or negotiation timeline, a specific engagement to use particular negotiations methods or to employ third-party intervention in case the negotiations break down etc.
3. Framework agreements. If you negotiated within the framework of a larger agreement or commercial relationship, then it may be possible that the terms of that agreement have specific provisions for the undertaking of negotiations, imposing sanctions or other remedies.
There is no clear-cut answer, but even if the commercial partner would prove the existence of an obligation to negotiate in good faith, that obligation should first be executed in nature (i.e. a return to negotiations) and any damages resulting out of its non-performance would then have to be proven.
All in all, I would recommend showing the LOI to a commercial-law specialized attorney if you suspect some terms may provide for more than a general wish to negotiate.
Now, you should bear in mind something else as well (based on your previous question): the Qatari company can sue you in Qatari courts. They could have quite a different interpretation of English law than English courts, particularly in this case, where there is no specific written law, and it is in their interest to hold for their nationals. So even if an English lawyer gives one answer, you might have the surprise that they come up trying to enforce a ruling of a Qatari court, which goes against what an English court would have decided. This is one of the pitfalls of private international law (also known as conflict of laws). The most appropriate thing in this regard would be to fight both in the Qatari court, and afterwards in the English court which will judge the possibility of enforcement in England, but of course your strategy would also have to take into account a costs-benefits analysis, particularly if the damages ordered (if any) are small.
I hope my answer was useful and look forward to your rating, which is essential to my activity.
Dr I L Vlad