When they told you to wait until court eviction they didn't mean literally take no action. They meant don't voluntarily move out. This is because you'd be voluntarily homeless and that means they don't have to help you. You can still bid on property and should do this, you never know you might get lucky and be allocated somewhere without having to use the homeless route. It can take months for court eviction to be put in place. You should continue paying rent.
You'll be initially moved into temporary housing, whatever form that takes. However shitty it is or however bad the area, you have to accept it or else you're making yourself voluntarily homeless again. It isn't necessarily going to be somewhere horrible though.
At some point your priority status will rise to homeless (so top priority banding), keep the council updated on your circumstances every step of the way using the bidding portal and this should happen automatically. While you're waiting to be re-banded you can still bid and should do so.
If you don't have any friends who can help you with storage (bear in mind anything fabric, like mattress or sofa, will go mouldy in a garage or shed) and if you're short of cash and won't be able to pay for a storage unit for furniture and personal possessions, then you should consider selling everything possible so as to get some money for it while you can, instead of having to pay the council £10 per item to take it away (unless you can drive it to the tip yourself) when you move out into temporary accommodation. You can book these collections if necessary by contacting the council, they'll put you through to the right department and take payment and organise a day to come collect the unwanted items. To give you an idea of what to keep/dispose of, temporary accommodation is likely to be a one bedroom flat at best and a hotel/hostel room at worst. The flats will be empty so you'll need eg bed and washing machine etc and will be able to sacrifice space to move about for choosing to store some possessions if you want to, the hotel rooms have beds already and not much room for storing anything else. There's no knowing which you'll get.
If you're skint and end up having to get rid of majority of your stuff, check out charities in your area helping to furnish new places for homeless people, you can apply for help whether you're in temporary or permanent housing, but usually can only apply once. They may also be interested in taking your items (if they're in good condition) to donate to others, which if you've not managed to sell them could save you the council's fee for taking them away to the tip.
Depending on the area you live and the availability versus demand for social housing, you could be in temporary accommodation anywhere from a few weeks to over a decade. You could also be rehoused out of area when you are allocated somewhere permanent. With the permanent offers you can usually decline 2 of them before you're in a situation of needing to accept the third one or be considered voluntarily homeless. This applies whether they've offered you one that you've bid on or a direct let (those are the ones they don't let people bid on, they just choose who to offer them to, usually people who have been homeless a long time or some other special circumstances). So before you decline anything, check the implications of doing so.
If you're placed somewhere legally unsuitable (for permanent housing) eg overcrowded or containing stairs when you can't walk etc and not just unsuitable in your opinion because eg it happens to be out of your current area, you have a short fixed timescale for officially complaining about that and if your complaint is upheld your homeless/priority need to move status will be reinstated. You won't be moved to temporary accommodation again, instead you'll stay in the property you're in but will be able to bid on other properties that are more suitable for you, having the additional priority status that comes from not being suitably housed. I think they're also obligated to look for a more suitable direct let to offer you, but I'm not totally sure about that part.