Something like Matcher possibly easiest, but can also see a FeatureJoiner + Tester solution alternative

Matcher though will put the group_id straight onto the output.  It just needs attribute1 and attribute2 to be named temporarily as a common attribute name.  Counter also here to give each row a unique Row ID, so that Matcher will not match the same row to itself in the Attributes That Must Differ parameter.

Now, the rules you’ve stated give a slightly different result.  Technically Rows 3 and 4 match twice in two separate groups,  They have a match first on England → England,  and a separate match on London → London and so Matcher, according the match rules, finds these rows belong to two groups, an England Group, and a London Group.   These can be filtered out if needed, but left as is.

Similarly, technically Rows 1, 7 and 8 also all belong to 1 Group, being the “Rom” Group rather than what you’ve got with only Rows 7, 8 in the Group.

Also the option of outputting the groups into Lists on the Matcher SingleMatched Port is also enabled to have options for handling the data this way through List operations.

Tidy up is a little more work to include and handle the NotMatched Features and give them a unique group_id but is something like this

Thank you this was such a big help! Thank you also for all the details :)