The new slots have been open since Good Friday for customers to order online shopping to their homes.
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These orders will be made with products from 270 larger Tesco stores.
It is the first time the supermarket has made online deliveries on Easter Sunday.
They are only available for what Tesco says is "our most vulnerable customers" to stock up on extra food and essential supplies over the long weekend.
This follows on from an announcement last week when the grocer said it was giving 75,000 vulnerable customers priority access to shopping slots.
Anyone who receives one of these orders will also get a free Easter egg and a card from the supermarket.
Usually all shops are closed on Easter Sunday in accordance with trading rules. This applies in England, Wales, and Northern Ireland but there are no restrictions in Scotland where shops will be open as usual.
A statement from the supermarket said: "We have been working hard to increase the capacity of our online delivery service to help more customers gain access to this service when they need it.
"We will be making 40,000 deliveries to our most vulnerable customers.
Tesco also confirmed last week that it increased the number of delivery slots to all customers by 150,000.
It is also adding more than 8,000 new slots a day and says it is working to add "hundreds of thousands" more home delivery and click and collect slots available.
But last week it said its online delivery slots were currently only available to 10 per cent of customers.
The majority of people therefore will still need to visit a supermarket in order to buy groceries.
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The supermarket is also donating 10,000 Easter eggs to children who are currently in hospital.
To meet the increased demand, the supermarket has already hired an extra 2,500 drivers, and 5,000 pickers.
Tesco stores are also opening later and instead of opening at 6am or 7am, stores with online grocery arms will now open from 8am.
Shops are still closing at 10pm (or earlier) in order to give staff more time to stock shelves and clean.
Tesco has almost 4,000 stores in the UK – use the online shop locator tool to find the opening times of your nearest branch.
It will be open on Easter Monday between 8am and 6pm.
Opening hours at Tesco will depend on the type of store you're visiting, so make sure you double-check your nearest branch's hours before making the journey via the online store finder.
Delivery slots are hard to come by for most customers but they are released at midnight so it might be worth checking back then.
We've listed the Easter opening hours for all the supermarkets in our guide.
Morrisons has now lifted its restrictions on purchases.
Aldi is set to axe its limits on certain products on Monday.
While Asda has launched a free prescription delivery service for some customers.
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