For UK residents, the normal procedure would be to prepare and file an application with the UK Patent Office. If an alternative strategy is employed National Security Regulations may be contravened; although it is possible to seek prior clearance to avoid this problem.
Most countries of the world operate a "first to file" system and, usually, once you have filed the initial application you will have "staked your claim" and any subsequent disclosure of the invention (as disclosed in the application) will not invalidate your patent rights.
Since the UK, like most countries, is a signatory of various International Conventions; the filing of an application with the UK Patent Office starts a 12 month period of grace within which applications filed in other signatory countries are treated as if they had been filed in those countries as of the date of the first UK filing.
An application may be filed with a minimum of formal documentation. But, you could subsequently be limited by what was, or was not, in the original documentation. Further, it will usually be worthwhile filing a set of "claims" and requesting that an official Search be undertaken. The results of the official Search are usually very helpful in deciding on the cost justification of extending the patent rights to other countries.
Within the first 12 months "top-up" patent applications can be filed (for any significant variations to the original invention. These, usually, need to be combined with the original by the end of the first 12 months. Thereafter, no further developments to the original invention can be added within the patent application.
The time taken to obtain the grant of full patent rights varies considerably from country to country. It can be as quick as 18 months or less. Typically it may take 3 to 4 years. If you get caught in post grant Opposition proceedings (which exist in some of the major patent application systems) you are likely to be in a state of uncertainty for very many years. In the worst case we have experienced the delay was more than 20 years - i.e. longer than the life of the patent !
Finally, beware that many patent application systems include a so-called "early publication" procedure whereby the content of your patent application is made available to the public (usually 18 months after your earliest filing date) long before you know if your patent will actually be granted or not.