If you are unhappy with your solicitor's service you can write to the Complaints Handling Partner and ask him to invoke his complaints procedure under Rule 15 of the Solicitors' Conduct Rules.
Like you, I am amazed that he has not taken a proof of your evidence much sooner.
With personal injury (and this type of medical negligence falls under pi), the limitiation period is 3 years. This is the time limit to which he refers. The form that he is talking about submitting to court is the issue of proceedings - ie a claim form - which is the start of formal litigation. The Limitation Act 1980 provides that (subject to certain exceptions) proceedings for pi must be started within 3 years. Starting proceeedings means lodging the court papers with the court for issue. Issue is the administrative process by which they are received by the court and stamped as issued. To be fully effective, proceedings have to be served. Under CPR Rule 6, proceedings once issued must be served within 4 months. In general they are normally served immediately, but you can wait up to 4 months to serve on the other party (6 if outside the jurisdiction).
Thus, what your solicitor is wanting to do, is issue proceedings and not serve them for a couple of months with a view to settling this through negotiation, I imagine. Colloquially known as protective proceedings (it protects your rights which would otherwise be statute barred). If it doesn't settle, you are then in the process of full litigation.