As D Stanley pointed out, rent and real estate prices are not always correlated. The Brexit vote was a clear example of that with property prices stagnating right after, but rent still increasing in London.
However, that is besides the point - rent is decreasing as well.
Rent negotiations work in the same way as any other negotiation. You need to know the market, your situation and your landlord's situation. If you can get a better deal than constant rent - you have an advantage. If your landlord is unlikely to find another tenant quickly for the same rent - they would lose money and are more willing to lower rent if you ask.
So the three categories:
1) Market. I'll talk about London here, as you didn't specify where in the UK you are. Rent is currently decreasing, however most rental and real estate agencies agree that it's the effect of the pandemic. Airbnb short-term holiday rentals are being pushed out into the long-term market to manage losses. You mention your rent review is coming up in a few months. First thing you have to think about is whether the pandemic and lockdown will end or ease by that time. If yes - your advantage will likely disappear. If no, you have to factor in extra moving costs, see below. Generally, I would not expect current prices to have any bearing on what you can negotiate for a September or later renewal, assuming the lockdown ends early summer.
2) Your situation. Here you have to figure out how bad will a move hit you personally. A typical move for me set me back around 1000 pounds - that's inventories, contracts, movers, deposit deductions as well as travel costs to do viewings. Note that during the pandemic you might be hard pressed to find cheap services - most rental agencies are "virtual" now, and movers aren't classified as essential business. Finding good alternative accommodation will be difficult if you can't leave your house.
3) Landlord's situation. They will be very hard pressed to find a new tenant for the same money during the pandemic. If you say that the property has been vacant for 2 months, then their losses are likely going to be 2-3x monthly rent in either decreased revenue or mortgage payments, maybe more.
All in all, you stand a decent chance if the timing is in your favor. You will likely be asked whether you want to extend 1-2 months in advance. You'll have a couple of weeks to think about it. Use that time to do some viewings of similar properties. If the pandemic just ended, the rents are still lower and you can do the move without much extra cost, you can simply say so to your landlord. Once they receive your offer, they'll do their own research on the market, and if they estimate their losses from looking for a new tenant and negotiating a new rent are too much, they'll give you what you want, or, more likely, offer mid-way. That's assuming everyone is cool-headed and diplomatic, a big ego on either side can make or break it. If, however, the timing is such that you cannot easily move out because of the pandemic, or that the market already reversed, you probably won't get your decrease.