I know this isn’t the right place but I can’t find a better thread. During the previous lockdown there were posts about what places were open in some way e.g. emailing Shannon’s and collecting at the back gate. I’ve just been in Jumping Bean for some presents. They are going to do a click & collect service through their website: https://www.jumping-bean.co.uk
Forest Hill Society in conjunction with FHTA (traders association) are running a Countdown to Christmas campaign to feature local shops and services using #ShopSE23 on both Twitter and Instagram. The idea is to promote one or more shops daily with special offers of Christmas gift ideas and get people to shop local. It’s slowly kicking off in mid-November, but keep your eyes out already.
Given Lockdown 2.0 part of that will be to feature exactly which shops will be open for takeaways, click and collect etc.
And in relation to answering the topic question, I know Shannon’s will be open as Garden Centres are exempt from Lockdown!
I can’t find the full list on the gov site at the moment but here’s an article from Sky News which lists the types of businesses that can remain open. Whether individual businesses will choose to remain open or not we’ll have to wait and see I guess. But in Forest Hill I suspect the supermarkets will stay open as now. Not sure if they will bring back restrictions on products or numbers in the shop at any one time etc.
It’s a bit wordy, but here you go (I’ve linked into the relevant part to save you scrolling too 
):