Dave, we are talking about Members of Parliament, i.e. the House of Commons. There are 650 members and we elect them directly. The government is then formed by the party with a majority of seats (or occasionally by an alliance of parties none of which has a clear majority by itself). The leader of the largest party becomes Prime Minister; he/she forms a Cabinet each member of which is responsible for a government department.
Each parliamentary constituency is based on or in a traditional local area with some adjustment for population size. For example, Northamptonshire is a mainly rural area with a few towns of varying sizes. Northampton, the main town, has a population of over 200,000 and for elections is split into two - I live in Northampton South so that's the MP I vote for. There are several other constituencies within the county boundary, and every few years the lines between them are redrawn so that the pop. size in each remains more or less equal. However, in some areas it's just not possible to produce a constituency with that many people - the Western Isles in Scotland, for example, are a traditional area with identifiable concerns so despite a fairly low number of people they get their own MP. In Northampton, it's fairly easy to get the ballot boxes from each polling station to a central hall to be counted but in the Western Isles that's not so easy - they have to use small planes, ferries, and occasionally rowing boats to transport the boxes and that takes time. Northampton South will declare its results hours before the Western Isles because the count is easier.
Our elections are run by a local official appointed for the purpose - the returning officer. He/she is responsible for ensuring the elections are run according to law and that every polling station is conducted properly. In addition, the returning officer must be present at the count and when the votes are counted, the returning officer will announce the results. There will certainly be a representative of local media present, either a newspaper reporter and/or local tv/radio. If the constituency is of national interest e.g. where the current prime minister lives or a seat which might tip the balance between parties, it's likely that national tv will cover it. But note that our local tv stations are all part of either the BBC's network or the ITV network so they pool resources - plus in cases like elections, both the BBC and ITV will share things like TV feeds - they don't both have to send camera crews to everything.
There are 64 million people in the UK.
You might like to read
http://en.wikipedia.org/wiki/Government_of_the_United_Kingdom and
https://www.gov.uk/government/how-government-works