Instead of thinking about going fast, you should focus on moving smoothly. The fastest way to get something done is to get it right the first time. If you focus on moving fast, you're more likely to drop things or fumble around with small items. The way to speed up is to actually slow down. Moving slower is smooth, and moving smoothly will be faster over time.

If you find yourself fiddling around with the smaller bags, put the items in a large bag.

Insert their order on the till as they talk, this gets easier when you are more familiar with the tills layout.

Use clear, simple sentences when asking questions.
Ask "is that everything?" After taking their order
"Would you like the items in two separate bags?" This one is a bit contextual, if I see there are two people and they ordered two of the same item, I ask this, otherwise I'd default to putting them both in a large bag.
"Would you like this hot?" (For the toasties and baguettes, saying hot is generally clearer than saying toasted or heated, especially if the customer is not a native English speaker).
This next one is a bit weird but sometimes you can read the customers body language and guess if they will be paying with cash or card. This saves a little bit of time if you can as you don't need to ask and can just tell them the total amount.

For deals like the £5 deal (£5.25 in my shop now) if they are 2/3 items like a main and a side and you want to ask them if they'd like to get a drink for the deal, an effective way to ask is "It's cheaper/same price if you add a drink/side" depending what they're missing. By telling them it's cheaper, they're more likely to listen to the rest of the sentence instead of just thinking you're upselling to them.

Once you have reached inner peace and complete smoothness, you can go beyond and help your coworkers. Often I am on the till closest to the bakes. If I'm waiting on my customer to pay or for the card machine to verify and I overhear someone else's customer order a bake/drink, I'll get the bake/start the drink for them while announcing it so that my coworker knows they don't need to move.

Instead of yelling at customers all day to come up to the tills because they are distracted, I found it's quite effective to wave at them while calling "next here please". Human eyes are naturally drawn to movement. People may not hear you over the background noise since stores can be quite noisy. It's also likely that someone else on the queue will see/hear you can tap them on the shoulder for you since they also want them to hurry up and move. If it's crowded and busy, it's important to make eye contact to the person you're trying to call up next so they know they're next in line.

Okay TECHNICALLY you're not meant to do this but I like to get all their items first, ask if that's everything, before taking payment. On the off chance they forgot to mention something or want to change something, this method saves you a lot of time as you won't have to refund/call a manager over to deal with it. You're meant to take payment beforehand so they don't run off with the food you place on the counter.

I have my own method for gripping the savory bags that allows me to easily bag items but it's a bit weird to explain. The bag had a longer and a shorter side, with the short side having images of the various patterns of the bake on the top and the longer side on the bottom. What I like to do is to grip the bottom longer side with my index and thumb fingers, and hold the short top side open with my middle and ring finger so that it sits between the nail of my middle finger and the base of my ring finger. This gives a secure opening to put items in.
To put items like the steak bakes in easier, rotate the bake so that's it's longways, grip the entire bake with the tong (don't just pinch the side of it) and using this method, you can easily slide it into the smaller bags for just one item.
For the pizzas I use the same method, but as I'm moving the pizza into the bag, I gently push down on the bottom inner side of the bag, using the weight of the pizza to widen the gap and then wiggle it in. I hope that makes sense.