Rugby Borough Council states that "Conservation areas protect areas of special architectural or historical interest", that Rugby currently has 19 of them, and that "You should always check with the council's development control team before carrying out work to a property in a conservation area." Those it names include Rugby Town Centre, Rugby School, Bilton, Bilton Road, Old Brownsover, Clifton Road with Hillmorton Road and Whitehall Road, and Hillmorton Locks. Its Article 4 Directions page lists four directions, at Top Road Barnacle, Land off Moor Lane Willoughby, Pear Tree Farm Willoughby, and houses in multiple occupation, and says nothing about windows or doors.
The Planning Portal states that planning permission is not usually needed for the "insertion of new windows and doors that are of a similar appearance to those used in the construction of the house". It adds that "If your house is in a designated area (conservation area, national park, area of outstanding natural beauty) there may be additional restrictions in place", and that a listed building needs listed building consent for any significant works.
On building control the same source states that "Since 1 April 2002 building regulations have applied to all replacement glazing", and gives two routes: "an installer registered with the relevant competent person scheme", who provides a certificate on completion, or an unregistered installer or do it yourself, "in which case approval can be sought from the relevant Building Control Body".
We would explain how you check the conservation boundary, any Article 4 direction and the proposed work before confirming whether permission is needed. The council's own line about ringing development control goes on the same page, with the link.