Anyone can pay the contributions, but its usually the applicant, since the applicant is the one who sought the permission and who would normally be either building the development or engaging a developer to build it on their behalf.
Where sell on occurs, unless the development had already commenced, it might be rash to assume that any contributions or levies had been paid.
The Conditions of Planning Permission requiring them usually begin with the wording "prior to the commencement ofi development" or similar.
However it is commonplace for people developing pursuant to a permission to resist paying the levies for as long as possible, despite the interest rates.
So even where development had commenced, the levies might not be paid, and a technical breach of planning might have occured.
In relation to any responsibility arising from professional involvement I would note the following; -
I believe there may be no strict requirement for a solicitor to advise a client in relation to the levies.
Even the least experienced layperson knows that permission is required for major undertakings like building houses.
Conditions are written in plain english and Planning Permission conditions are not hidden knowledge.
The Planning Register is available to the public and the permission would be the cause of the price paid for the property in many cases.
Therefore it is a reasonable assumption that the purchaser became or made themselves aware of the permission plus any conditions attaching to it.
However, if the purchaser formally requested advice or professional comment on the permission at any time, there would be a duty of care arising I believe such that the professional should advise the purchaser from within their competence.
This might go far beyond the matter of levies or contributions - issues of rights of way, discrepancies between the site plan and site survey, information not submitted of a material nature [an underground watercourse for example] might all require specific advice to be offered.
The onus on payment goes with the commencement of development.
The person in control of this, or the persion who may breach planning law if the levies are not paid over, and who are therefor liable under law, normally ensure that the levies are paid.
A solicitor in conveyancing mode, not asked to advise the client in detail on the purchase, might be well advised to say nothing about the permission.
I hop this helps answer your question.
ONQ.
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All advice on AAM is remote from the situation and cannot be relied upon as a defence or support - in and of itself - should legal action be taken.
Competent legal and building professionals should be asked to advise in Real Life with rights to inspect and issue reports on the matters at hand.