Cesere is correct here - as usual, the rest of you are talking bonkers bruno rubbish.
Any worker can join any union they like irrespective of industry or trade, or recognition agreements.
However - unions can and do refuse to accept them for a variety of reasons.
Also there are agreements policed by the TUC around spheres of influence among TUC affiliated unions so that companies and areas can be carved up between unions or allocated to individual unions - sometimes sections of workers will be "traded between unions" for various reasons.
Furthermore an employer only has to recognise one union per bargaining unit, but can represent more if they wish - in the public sector this gets more complicated with national bargaining being conducted sometimes by many unions with the employer side sometimes with just one or two. This is often illustrated by the different colour books of T&Cs.
The fire service is an interesting microcosm of how this works
Operational staff - firefighters and control room staff are on 'Gray Book' which is negotiated nationally and for which only the FBU has recognition. Back room and facilities and maintenance staff are all on 'Green Book' and are part of national local government T&Cs and recognition exists locally with the individiul fire authority. UNISON is the only union in 99% of brigades, however some brigades do recognise GMB for historical reasons alongside UNISON, and in at least one brigade GMB members are "looked after" by UNISON despite being GMB members in a strange little local agreement between the two unions.
Now within the Firebrigade you also get the Fire Officers Association who don't have recognition and will recruit among Gray and Green book staff and can provide representation at an indidividual level - no one can stop them doing that, but they have no input into negotiations or consultation for either group of staff.
So broadly speaking you can have recognised unions for an entire service or employer, or recognised unions for local bargaining units, you can also have unions which are not recognised but are active within a sector, and unions which are not recognised within a sector.
Again in the public sector in particular (but also private - the maritime industry is fascinating) this is complicated by TUPE where generally workers will carry their union recognition across from their old employer to the new one as long as they remain a discrete group.
ETA: generally a union will turn people down for two reasons. 1 becasue they don't believe they would be able to service that person so for example if a worker in a little corner shop applied to join UNISON they should be sent a letter advising them to join Usdaw, because Unison doesn't have the capacity to provide adequate representation (this won't often happen because if they join online it won't often be picked up. 2. Sphere's of influence - Usdaw wouldn't be happy if UNISON started recruiting shop workers. Having said that Usdaw does compete with Unite, Community, and the GMB in the retail sector especially among distribution workers.
So to sum up Ceseare is correct, despite any examples you can come up with where you think she is wrong.
