The adopted Bedworth Conservation Area Appraisal and Management Plan of 2022 states at 9.3.6 that "UPVC or plastic windows and doors are not a traditional or vernacular material and are unsuitable for use in historic buildings. The replacement of uPVC windows and doors with timber products is encouraged", and at 9.3.7 that for steel or aluminium windows "the appearance and detailing of these windows is not usually in character with most historic buildings. Their use is discouraged unless used in the original building design." At 5.10.4 it records that "Modern buildings have uPVC windows, also several historic buildings have had their windows inappropriately replaced with uPVC units."
The same appraisal states at 10.1.4 that "The 2021 review identified; 53, 55, 57, 59, King Street, Bedworth, and 24, 26, 28, 30, 32, 34, 36 Chapel Street, Bedworth as buildings where certain permitted development rights should be suspended", and that "The Council will keep the proposed Article 4 Direction under review". That is a proposal, and a page should say as much. Nuneaton and Bedworth Borough Council also states that "You will need to obtain Listed Building consent if you wish to demolish a listed building or alter it in any way which will affect its historic fabric or character".
The Planning Portal states that "An external window or door is a 'controlled fitting' under the Building Regulations" and that "Since 1 April 2002 building regulations have applied to all replacement glazing". It 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". GOV.UK names Blue Flame Certification, CERTASS, Certsure, Fensa, NAPIT and ASSURE for replacement windows and doors in existing dwellings.
We would explain how you check the conservation boundary, any Article 4 direction and the proposed work before confirming whether permission is needed, with the appraisal's own paragraph numbers cited beside the quotations.