score:5
Union citizenship and the rights (such as freedom of movement) that comes with it attach to a person, not to a particular passport.
Not having a Czech passport (or identity card) simply means it will be somewhat more cumbersome for you to demonstrate that you have those rights to authorities than if you could just show a standard document. But it does not mean that you don't have the rights, and if you need to rely on them in your dealings with the UK government, the UK is obliged to let you prove "by other means" that you have them:
Where a Union citizen, or a family member who is not a national of a Member State, does not have the necessary travel documents or, if required, the necessary visas, the Member State concerned shall, before turning them back, give such persons every reasonable opportunity to obtain the necessary documents or have them brought to them within a reasonable period of time or to corroborate or prove by other means that they are covered by the right of free movement and residence.
Directive 2004/38, article 5.4.
(As written this appears to only apply to actually crossing the border. But I'm pretty sure it also has to hold analogously for relying on your rights after you have entered).
Note that private entities such as banks, employers, landlords, airlines may have a more restricted view of which kind of documentation for your citizenship they will accept than the government can get away with.