A quick trade deal means the country with the smaller economy being forced to accept the demands of the larger economy in return for the speed of the deal.
You don't want a quick deal if you're negotiating with the US. Unless you're not bothered about food safety, environmental standards, rules on procurement of public services (this means NHS).
One example. Chicken in America is usually washed with chlorine. You can't sell chlorine-washed chicken in the EU. The US chicken industry wants to sell its chicken internationally without having a separate chlorine-free production line. So the US puts something into a trade agreement with the UK that says chlorine-washed chicken is OK. The UK wants a quick agreement so says yes to that so it can improve the deal on a bigger priority like financial services.
Apply the chicken example to basically every category of goods or services.
If you're a single bloc negotiating on behalf of 28 countries you're more likely to be able to say no to stuff you really don't want and other countries are more likely to say yes to the things you do want. That's because other countries have much stronger incentives to get a deal with you so they can do more trade with you than if you're a single country alone.
File this one under things I never thought about before the referendum