if the Beeb ditches the Met O, the Someone Else they use will use the same data the Met O would have used, which seems a bit of a merry-go-round. So I've obviously got it wrong. I think Peter T can sort us (or me, anyway - everyone else may know what happens) out - please, Peter!
No Michael, you've got it right! As the national weather service, the Met Office ("MO") organises (and in many cases funds) the collection of data from official UK weather stations, ocean buoys, UK shipping, etc. All these data are shared internationally via the Global Telecommunication System (GTS) of the World Weather Watch, under the auspices of the World Meteorological organisation. All the data collected globally (including measurements from satellite borne instruments) are used in global atmospheric simulations ("models") which are produced by agencies such as the MO using some of the world's most powerful (and expensive) computers. These MO data and simulations are freely available to all participating met agencies but not, at least from the MO, directly to the public.
Until modern times the Met Office was fully funded in it's role by the government (coming under the RAF budget if I remember). However nowadays they are required to have a profitable commercial arm and sell their services to diverse customers like people moving oil rigs, people selling ice cream, ...and the BBC. If you pay them enough you will get forecasts tailored for your own specific requirements by teams of (human) forecasters who are informed by the regionally detailed output from the global computer models.
A major problem for the Met Office in trying to operate commercially is that in the USA, data and atmospheric model forecasts produced using public funding are considered "public domain". Thus all the data (including that collected by the Met Office) and all the information from US National Weather Service global atmospheric models are available for free. In most cases it is these NWS distributed data and model forecasts which are used by weather sites on the internet, for example xcweather and others. The NWS forecasts cover the whole globe with increasingly fine resolution. However when you go on the web and ask for a weather forecast for a specific place, what you will get is an interpolation of results from the nearest model grid points. (Internet sites such as iGrib are slightly different in that they tap into the stream of data on the GTS and display the "gridded binary" representations of observations and model forecasts.)
All these free data can be used by the commercial forecasting companies, who neither collect met data nor (as far as I know) run global forecasting models, but who will compete for the BBC contract. Unlike the MO they can concentrate all their human resources into interpreting the forecasts for their users.
Not fair you may say! However I personally find more and more that I am disappointed with the accuracy of publicly available MO forecasts (including the shipping forecast which is paid for by the MCA). Often I can do better for my purposes (i.e. sailing Seatern) by looking at the pressure charts and using the observations provided by xcweather on the web. I suspect this is because the Met Office is constrained by its available resources on relying too much on the model output without bringing in the local knowledge and interpretation which, at one time, human forecasters provided. A commercial firm forecasting for, for example BBC South, might well do a better job than the present "weather presenters" who seem to rely purely on the MO forecast output and who are trained as TV performers rather than weather forecasters.
so, that's my rant on the subject, you did ask Michael!