Hi thank you for your question. Please remember to RATE my answer OK SERVICE, GOOD SERVICE OR EXCELLENT SERVICE so I can get credited for my time.
In respect of asking for a write to appeal, this will depend on the reasons you included in your application and the reasons on what your appeal will be based on, if your application was refused for you not meeting the requirements of the rules and the home office refusing to exercise their discretion then even if you write a letter to the home office they will most probably not grant you a write to appeal.
If however, the only reasons for not granting you the right to appeal was because you did not submit the application in time then yes there is a chance that the immigration officer may allow you a write to appeal but from experience they can be very difficult to deal with.
I do believe that you should submit the letter to the enforcement officer stating that you are hoping to either appeal or submit a new application. The point to note here is that the enforcement officer is only interested in removing you from the UK and the best way to prevent that would be to either 1) Appeal (if right given) and submit a copy of the appeal and the grounds of appeal to him to indicate that he should suspend any removal proceeding pending the outcome of the appeal or 2) Evidence of a letter of receipt in respect of your application to the home office, which again will mean that he will stop any removal proceedings.
There is nothing wrong in doing what you have been advised but, what I would ensure in that firstly you will have to convince the immigration officer who made the decision that your application was actually made in time and not out of time, so this definitely needs to be contested because it will have an effect on your Tier 2 application.
In respect of a letter being drafted to the home officer, unfortunatley we are unable to draft documents, but I will give you a few points which you should include in the letter:
1) Need to state your intention to either appeal of submit a new application.
2) state reasons that the original decision was incorrect and that you have submitted a letter to the immigration officer contesting the decision
3) You would be grateful if the enforcement officer could suspend any removal action until a decision is made in respect of your appeal/and or tier 2 application.
4) State that you will forward the enforcement officer with any reply as soon as you receive correspondence from the home office.
5) You should state that you feel that you are genuinely being preventing from exercising your right of appeal due to an incorrect decision and are willing to take the matter as far as possible to obtain a favorable decision.
6) State that you would be grateful if they inform receipt of your letter and ensure you send it recorded delivery.
This is what you need to include in your letter to the enforcement officer. The fact is that they are of the view that you do not have a right of appeal , so yes you should keep them informed of what steps you have been taking and also that you have written to the immigration officer and expect to obtain a reply soon.
I hope this answers your question if so kindly rate my answer positively so I can get credited for my time. If however you feel that the answer does not cover all the points raised in your question please DO NOT rate my answer negatively I will be happy to answer further questions until you are satisfied with my answer.