You could but are not obligated to. You need to show the embassy that:
- there is a family relation, by marriage --> mariage papers (plus translation so the embassy can verify the content of the documents themselves).
- ID the both of you via a (copy of) passpors so they can match the names on the mariage papers plus confirm that you are an EU national (UK citizen) and she is not.
- That she will join you on the trip to an other EU/EEA country then the one you are a national of. This could be a written confirmation by you that your wife will join you to travel to France/Germany/Spain/... . But you could include a reservation of hotelbookings, flight/ferry etc. If you already got those I'd include them. If you don't I'd cover this in the letter: we will depart by *transport* but will book later (or on departure at the counter?) and find some place to sleep in hotels/campsites/... as we travel around.
- Medical travel insurance, proof of sufficient funds etc. is something they cannot ask for. They cannot refuse on ground such as "no sufficient ties to the homecountry: risk of failure to return in time" etc. They could decline if they suspect a sham marriage, her or you being a risk to national security (
) , bot being able to show that you are who you say you are etc.
