I am in the same situation as you. 3 month old, was 6 weeks pregnant when we went into lockdown, no family, have a 2 year old toddler. Its miserable sometimes.
However, I do put her upstairs once she is asleep at night and watch her on the monitor so me and DH can sit together and chat. I go on a walk every day. Yes, its freezing, so I wear 2 jumpers, tights under my jeans, I have a pair of sketches that I invested in, and I just walk very fast. It does wonders for the head. If you want to be brave you can join an app called MUSH and see if any local mums want to walk with you. You are allowed do that.
I try to see mat leave as a time for my baby to have me at home. Yes I am cripplingly lonely, hence why I am on MN, but i try to just give my kids my attention and think i will never have this time with them again, so i will enjoy cuddles and playtime .... or some days I might just have a wine at 5PM because it's been bloody relentless. I want my softplay, my baby groups, my church group, my NCT meetups that I had with DD1. But, I cant, so I have to make the best of it.
Put the baby upstairs or in a cot in the sitting room, sit with your DH, make it a priority. Go for the walks, even if it's cold. Get the app if you like. Try to hold out for spring and organise a picnic or more walks, anything with anyone you know who has a young baby. I promise, they are all craving social interaction. Be brave, ask them when the time comes. But I know it's tough. Very tough, and very lonely 