Andy - this can be foreboding but underneath all this there is a process (generally considered biased towards the developer - sadly), the primary challenge is to understand the rules of the game (Planning Policy & Guidance), the lexicon of planning speak, and how one goes about making a valid objection (i.e. one which, as others have flagged above, is relevant in the context of local planning policy & controls). I would suggest:
1- For starters, is the letter you have a formal advice from the Council or just an advice from the property owner(s)? Or perhaps someone acting on their behalf - perhaps the plot is to be sold conditional on getting PP?
2- Assuming it’s an official letter, check the timeline for responses. As the construction of a dwelling in a rear garden, I strongly suspect the local Council will not regard as a ‘Permitted Development’ (one which doesn’t require formal PP via C’tee) and it will require a full Planning C’tee.
3- Contact other local residents and seek out their views. Let’s assume their thoughts are the same re precedent in the locality (being mindful of situation of the plot/access et al).
4- Contact your local Councillor and flag with them. FYI, in general, Councillors are Chinese-walled from Planning Dept’s to avoid conflict of interests amongst other things, so they may have only just have learned of this too.
Ask them first by enquiry though, as if they are a member of the Planning C’tee, they may not be able to become involved and may nominate a proxy.
Assuming they can engage, get objecting local residents to engage with them individually.
5- Look up the local Council website (contact Planners as needed) and get a copy/print of the Local Plan or equivalent (note the noun), as this is highly likely to include all governing local development principles and controls. These can be quite broadly drafted - I think what you are looking at here is an in-fill site and there is sometimes specific guidance around these. The principles will often be written/expressed with guidance/instructional narrative (councils have to sign up to ‘Plain English’ too).
A word of warning - many local authorities (LAs) are under pressure to consent to new residential developments at the moment given pressure to build post the publishing of the National Planning Policy Framework in 2019. But - the latter doesn’t give carte blanche to developers.
6- Try and frame objections tested against local development controls i.e. as per the principles in the Plan document. The more local residents object the better.
– as a group, you may wish to engage a planning consultant (£’s not cheap) and a local councillor is usually the route to go, especially if you are in what sound like a ‘conservation area’ (with a very small ‘c’ - not a formal one?).
And be forensic, take photos to support contents & submissions - really think around & even outside the box. The (professional) skillsets of neighbours may help?
Around where I live, an opportunistic developer tried something on and the residents won!
Do ask more if you want.