4 of the 12 carriers here run their own network, and 8 rent space on one. giffgaff runs on O2, Tesco Mobile runs on O2, iD Mobile runs on Three UK, VOXI runs on Vodafone UK, SMARTY runs on Three UK, Lebara runs on Vodafone UK, Lyca Mobile runs on EE (via BT Wholesale) and Sky Mobile runs on O2. A carrier that rents a network often has its own APN, so copy the one on its card, not the host's.
EE, O2, Vodafone, giffgaff, Tesco Mobile, VOXI and Lebara use a username and password in the APN. For the others, leave both fields empty: a username where none is needed can stop data from working. Where an authentication type is given: EE uses PAP, O2 uses PAP and giffgaff uses PAP.
All 12 carriers list separate settings for picture messages (MMS). If texts work but photos in messages do not, those are the values to check. Vodafone also has a second APN for some plans or devices, shown on its card.
The carriers here use the mobile country code 234, the first three digits of every network code in the United Kingdom. Android usually fills in the MCC and MNC from the SIM, so you rarely need to type them.
Visiting the United Kingdom with your own SIM? Keep your home APN: roaming data still goes through your home carrier. You only need these settings with a local SIM bought in the United Kingdom. Or skip the SIM shop with a United Kingdom eSIM, which sets its own APN.