Savings accounts generally don't come with a card. These days you would normally access your savings by transferring to/from a current account.
The savings accounts offered by the high-street banks (like the ones you've named) generally offer poor rates of interest.
There are various sites on the web that collate the details of the accounts offered by the various banks/building societies.
@normaw has pointed you at one of these sites; there's also
The best rates tend to be from banks you've never heard of. In many cases these are well-established banks whose business is mainly in other areas -- for example, in specialised lending (car loans, commercial mortgages), or dealing with businesses rather than individuals.
But as long as they are covered by the
Financial Services Compensation Scheme any deposits of up to £85,000 are protected in full.
The best rates tend to be on accounts that have restrictions on access -- for example, they restrict you to no more than 3 withdrawals per year, or you need to give 30 days' notice of withdrawal. But some accounts do pay good rates with instant access and no limits on withdrawals. You just need to check the terms and conditions.
Note that in some cases, "easy access" can mean that withdrawals are processed the same day if requested before a specific cut-off time, and that requests after that point are paid the next working day. (Again, you need to check the Ts&Cs.) So you can't rely on money being transferred instantly in the way that you generally can with the high-street banks.
Re tax, interest is paid without tax being deducted. If you pay tax at basic rate, you can earn up to £1000 of interest a year without needing to pay tax on it; the allowance is £500 if you pay tax at 40%; but there's no allowance if you're taxed at 45%. So for most people, you won't pay tax on interest. If you do need to pay tax, HMRC generally collect this by adjusting your tax code.
See
Tax on savings interest (gov.uk) and
How tax on savings and investments works for more information.