Thanks for your patience.
As I say a ten year ban is usually only enforced in the even that a person is apprehended, detained by the UKBA and then disputes removal in a tribunal. can only assume that they regard your previous lack of disclosure with regard to not completing the form correctly as to you family as a deception (for which they are also permitted to levy bans).
It may be a mistake by the UKBA. They do make them frequently, so unless there are some applicable circumstances in your particular case which I do not know about I don’t think you should regard your situation as quite as desperate as the letter suggest.
I would not appeal the current application. I would instruct a UK based solicitor to prepare an application for a visitor’s visa on your behalf. The reason I would not appeal is that you have not submitted sponsorship declarations from your family and would not now be permitted to adduce them as evidence on appeal because only evidence in existence at the time of application is permitted. Thus, your starting position would be much, much poorer than it need be.
This is a statutory declaration sworn under the Statutory Declarations Act 1835, it carries more weight than a simple letter of sponsorship. It would state state terms of his visit, that you are to return at the end of it, that they shall accommodate you and shall pay the costs of any unforeseen expenses that should occur during your stay so that neither of you will need to access public funds.
This should be submitted with your application along with a detailed sworn statement by you which refers to and annexes all of your documentation. It should also contain a detailed explanation of your misunderstanding of the question asked in the earlier form and that this was an honest mistake which should not be considered prejudicial to your application.
In addition I would ask some persons of authority, both here and where you are, to execute character references sworn under oath to submit with your application.
It may be that the UKBA refuses this application as well. Rightly or wrongly the UKBA in my experience tends to place application from Nigerian citizens in a high risk category and your earlier mistake does little to persuade them otherwise. If they do refuse the application then you should appeal but you will at least be appealing from the strongest possible starting position, which is important. You should then instruct your solicitor to act on appeal together with a UK barrister to appear at the hearing itself.
If you wish for me to provide you with further guidance on any question you may have in the future then please submit a further question to the board requesting me either by my profile or by marking your question. “FAO Tom”, and I will be happy to help.