Your HP 2810-24g does have basic Layer 3 capabilities, known as Layer 3 Lite, and it could be used as a router.
All you have to do is update your new VLAN config, by assigning an IP address to the VLAN interface (known as SVI in Cisco parlance):
myswitch(config)# vlan 20
myswitch(vlan-if)# ip address 188.8.131.52 255.255.255.0
When two or more VLANs have an IP address, your switch is a router in pectore.
In order to enable routing in CLI, give this command in global config context:
myswitch(config)# ip routing
myswitch(config)# ip default-gateway A.B.C.D
A.B.C.D is you firewall IP address.
Remember to add a static route to the firewall for new LAN segments that are reachable through the switch/router, and please do remember to apply source NAT to packets leaving the firewall directed to Internet.