Intransitive prepositions
Some words which look, sound and behave like prepositions can also be used without a following noun phrase. In traditional grammar they used to be considered adverbs, or occasionally adjectives, but in modern grammars are just called 'intransitive' prepositions. Here are some examples:
- The man outside the building. [preposition with noun phrase complement]
- The man outside. [intransitive preposition]
- The morning after the party. [preposition with noun phrase complement]
- The morning after. [intransitive preposition]
This is what is happening in the OP's example:
- The Conservatives opposite us. [preposition with noun phrase complement]
- The Conservatives opposite. [intransitive preposition]
The OP's example is a case of a noun postmodified by an intransitive preposition. As shown, the preposition could equally have been used with a noun phrase complement.
There is an adjective opposite. However, this is not the adjective, but the preposition!
Some tests
Note that these prepositions behave just like prepositions and nothing like adjectives!
Nearly all spatial prepositions can be used to freely postmodify nouns. The same is not true of adjectives:
- *The car big (ungrammatical)
- *The people local (ungrammatical)
- The car in the garage
- The people nearby the entrance
Whereas adjectives can often be modified by the adverb very, prepositions cannot:
- very big
- very local
- *very in the garage (ungrammatical)
- *the Conservatives very opposite (ungrammatical)
Prepositions can often be modified by the specialised adverb right. In standard Englishes, adjectives can't:
- *the right big car (ungrammatical)
- *the amenities are right local (ungrammatical)
- The Conservatives right opposite
- The car is right in there.
These tests show that 'opposite' in OP's example is a preposition, not an adjective.
This data also shows that OP's example cannot be a case of an appositive because appositives are usually noun phrases.