Requesting a CAT 2/3 due your assessment of the Wx is always an option. Most major airports in EU, certainly UK, will go LVO when cloud base or vis starts getting low. For UK I believe the standard is <300' or <1100m. Correct me if wrong. It makes commercial sense for ATC to avoid G.A's. If you are CAT 3 authorised why stop at CAT 2? It could be a/c type. What irritated me in Germany is when the Wx went 200' or 350m regional ATC declared the airport CAT 2. I asked if there was a problem with our destination, as it was a CAT 3 airfield. The reply was the Wx was only CAT 2 and so that was the status. Of course, when we asked the TWR for CAT 3 it was no problem as the protected area is the same. They had no method for downgrading CAT 1 to only CAT 2. It was CAT 1 or CAT 3. Just confusing pedantics for area control.
In my experience if the weather gets DH +100' or VIS = 150% RVR and CAT 2/3 is available why not request it. ATC have no reason not to allow it if traffic and airfield configuration allow time to organise it. Therein lies the rub. If possible call the airfield 15mins in advance.