The majority of motoring offences including that of "using a motor vehicle uninsured against third party risks" are summary offences i.e. they are dealt with by the Magistrates' Courts.
In England & Wales, under
S.127 Magistrates' Courts Act 1980, except where statute provides otherwise (doesn't in this case), an information must be laid within 6 months of the commission of the alleged offence, from which point court proceedings may commence; if the laying of an information falls outside this 6 month limit then the prosecution is time-barred (although it may be possible for an extension to be granted in exceptional circumstances). Similar legislation exists for Scotland and NI.
Since it is feasible that the issuance and serving of a Summons may take a few weeks after an information has been laid, then it is
likely (but not definite) that the maximum time to expect to receive a Summons is less than 7 months from the date of offence, after which time the case may not be heard by the Court.
Those summary motoring offences excepted from this "6 months from date of offence" limitation, but for which proceedings may be brought within a period of 6 months from the date on which evidence sufficient in the opinion of the prosecutor to warrant the proceedings came to his knowledge, are listed in this
Schedule (appended with the note 'Section 6 of this Act'). In any event these offences must be prosecuted within 3 years.