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In 2020, women's cricket in England was restructured, creating eight new 'regional hub' teams, with the intention of playing both 50-over and 20-over cricket. The team, then known as Lightning, were one of the sides created under this structure, effectively replacing the Women's Cricket Super League team Loughborough Lightning and representing the East Midlands, partnering with Nottinghamshire, Leicestershire, Derbyshire and Lincolnshire, as well as Loughborough University. The side was to be captained by Kathryn Bryce and coached by Rob Taylor. Due to the COVID-19 pandemic, the 2020 season was truncated, and only 50-over cricket was played, in the Rachael Heyhoe Flint Trophy. Lightning finished bottom of the North Group in the competition, winning two of their six matches. At the end of the season, five Lightning players were given full-time domestic contracts, the first of their kind in England: Kathryn Bryce, Sarah Bryce, Bethan Ellis, Lucy Higham and Abigail Freeborn.

The following season, 2021, Lightning competed in both the Rachael Heyhoe Flint Trophy and the newly-formed Twenty20 competition, the Charlotte Edwards Cup. In the Charlotte Edwards Cup the side finished bottom of their group, losing all six of their matches. In the Rachael Heyhoe Flint Trophy, Lightning finished fourth in the group of eight, winning three of their seven matches. In the final match of the season, Lightning scored 320/6 in their victory over Central Sparks, with the Bryce sisters, Kathryn and Sarah, sharing a 207-run partnership, the highest across the competition. Lightning bowler Kirstie Gordon was the leading wicket-taker in the competition, with 16 wickets. Rob Taylor left his role as Head Coach at the end of the season, and was later replaced by Chris Guest.

Lightning again finished bottom of their group in the Charlotte Edwards Cup in 2022, but did win their first Twenty20 match, beating North West Thunder by 5 wickets. In September 2022, it was announced that Nottinghamshire CCC would become the new host of the team, replacing Loughborough University, and it was also announced that the name of the team would change. The side finished sixth out of eight in the 2022 Rachael Heyhoe Flint Trophy.

In November 2022, it was announced that the team had been renamed The Blaze. Kirstie Gordon was named as the side's new captain in April 2023. The side went unbeaten through the group stage of the Charlotte Edwards Cup, but lost in the final to Southern Vipers. They also qualified for the knockout stages in the Rachael Heyhoe Flint Trophy, finishing second in the group, before defeating South East Stars in the play-off. However, they again lost to Southern Vipers in the final.