As I understand it, to teach for the PPL you require at least CPL theoretical knowledge, as laid out in Part FCL 915, otherwise you are limited to the LAPL.
FCL.915.FI FI — Prerequisites
An applicant for an FI certificate shall:
(a) in the case of the FI(A) and FI(H):
(1) have received at least 10 hours of instrument flight instruction on the appropriate aircraft category, of which not more than 5 hours may be instrument ground time in an FSTD;
(2) have completed 20 hours of VFR cross-country flight on the appropriate aircraft category as PIC; and
(b) additionally, for the FI(A):
(1) hold at least a CPL(A); or
(2) hold at least a PPL(A) and have:
(i) met the requirements for CPL theoretical knowledge, except for an FI(A) providing training for the LAPL(A) only; and
(ii) completed at least 200 hours of flight time on aeroplanes or TMGs, of which 150 hours as PIC;
(3) have completed at least 30 hours on single-engine piston powered aeroplanes of which at least 5 hours shall have been completed during the 6 months preceding the pre-entry flight test set out in FCL.930.FI(a);
(4) have completed a VFR cross-country flight as PIC, including a flight of at least 540 km (300 NM) in the course of which full stop landings at 2 different aerodromes shall be made;
(c) additionally, for the FI(H), have completed 250 hours total flight time as pilot on helicopters of which:
(1) at least 100 hours shall be as PIC, if the applicant holds at least a CPL(H); or
(2) at least 200 hours as PIC, if the applicant holds at least a PPL(H) and has met the requirements for CPL theoretical knowledge;
(d) for an FI(As), have completed 500 hours of flight time on airships as PIC, of which 400 hours shall be as PIC holding a CPL(As);
(e) for an FI(S), have completed 100 hours of flight time and 200 launches as PIC on sailplanes. Additionally, where the applicant wishes to give flight instruction on TMGs, he/she shall have completed 30 hours of flight time as PIC on TMGs and an additional assessment of competence on a TMG in accordance with FCL.935 with an FI qualified in accordance with FCL.905.FI(j);
(f) for an FI(B), have completed 75 hours of balloon flight time as PIC, of which at least 15 hours have to be in the class for which flight instruction will be given.
Hope that helps.