A firm sent me and offer, I accepted the offer and this acceptance was acknowledged by the firm
After a few weeks, I got a call from the firm informing me that the offer is still pending approval ?
I have had two related experiences in the U.K.: One, at a major company they made an offer, then the budget was cut. The opinion of the managers discussing this was that they prayed the offer wouldn’t be accepted, because they would have to hire the person and someone would be in trouble with their budget.
Two, at one company they hired someone and before his starting date, the whole department including the manager hiring him were laid off. The guy arrived and nobody knew who he was. He stayed there for six years.
Making you an offer without having approval is bad. It’s reckless and a major red flag. (Both cases I mentioned the hiring was approved and then things went wrong). I’d strongly recommend that you continue or restart your job search. And if you have given notice, talk to your old company. They might be happy to keep you longer. Or they are not, but worth trying.
Yes it is possible for a firm to back out of an offer. This might be breach of contract, but notice the following points:
There is usually an initial probationary period which can be terminated with notice of a week. If they cancel the offer more than a week before the planned starting date, then that is an end of it. (It might be argued that the week's notice only applies after you have started, but that would depend on the exact wording of the contract.)
If you hadn't agreed a starting date, you didn't have a contract - you were still negotiating the terms.
Even if they have breached the contract, your losses are, at most, one week's wages (because they could have waited till you started, and then let you go). It is unlikely to be worth suing them for a week's wages - if you have sued an employer, you will be less attractive to other employers.
I presume you have given notice at your previous company. I suggest you return to job hunting with renewed vigour. I wouldn't try to return to your previous company - but it might be worth investigating if they would be interested in employing you as a short-term contractor (it depends how valuable you are to them).
If the offer was either unconditional or you've met all the conditions specified in the offer than it became a binding contract when you accepted it - if they withdraw it now you can sue them for breach of contract but it would be difficult to prove losses of more than the wages you would be owed for statutory notice period (1 week unless the contract specifies more) if there are unmet conditions then they can withdraw it freely.
Is it worth suing for that week's wages? Maybe - it's not going to be a fast process nor a cheap one and you might not come out any better off.
Depending on the circumstances you may be able to do more than this - if you have evidence that a withdrawal of an offer was due to discrimination (specifically for a protected characteristic) then you can take them to an employment tribunal.
Hopefully this may not actually come to the point of a withdrawal (assuming I'm reading your post correctly it's only referred to as "pending approval" at this point) and things will work out.