This is a battle of the forms question, don’t discuss the issue of who sought planning permission as it is not relevant. The main point are as follows:
1. Neil’s letter is obviously an offer. It is an offer to contract on the standard terms. It does not matter at this stage that he forgot to include them - it is possible to accept this offer without knowing what the terms are!
2. Tony’s letter is not an acceptance. Acceptances must mirror the offer, and Tony’s letter does not mirror since it includes different terms on planning permission. It is therefore prima facie a counter offer.
3. A valid counter offer terminates the original offer (meaning it cannot be accepted later). However, offers must be actually communicated to the recipient - the postal rule applicable to acceptances does not apply. Since the letter has not arrived, Tony has failed to make a counter offer. This means Neil’s offer is still valid and capable of acceptance.
4. Tony then told Neil he accepted his offer. A reasonable person would not know about Tony’s subjective misimpressions, so the fact that Tony thought his letter was received is not relevant. Since the original offer is still valid and a reasonable person would understand Tony to be accepting it, there is a contract (assuming intention to be bound and consideration, which you rightly point out aren’t a big issue here). The timing of acceptance was when it was communicated to the secretary (Neil’s agent).
5. Since there is a contract on Tony’s standard terms, you then need to consider if the planning permission clause was incorporated. Consider whether it is an unusual or onerous term, and then whether it meets the test for incorporation.
6. If the term is incorporated, it may still be void for unfairness under the ‘standard terms’ section of the Unfair Contract Terms Act 1977. Apply those tests to see if the term is void or not (noting in particular whether the term is a type of clause which is regulated by UCTA in the first place).
6. If the term is incorporated and valid, Tony is out of luck. If it is not, he is likely still out of luck. This is because the absence of this term does not mean his term about satisfactory permission would be included. Instead, the court would interpret the contract using the usual rules (officious bystander, business efficacy tests) to see what the contract objectively means. In the absence of any term talking about planning permission, it is unlikely that a reasonable person would interpret the contract as allowing Tony to demand a discount to take into account the extra cost. The price is the price.
That’s the structure I’d take and the issues I’d address.