Everything after the cables come out of the meter are your responsibility. They are two completely separate jobs. Your energy supplier will handle replacing the meter, you’ll need to contact a local electrician to replace the consumer unit.
There’s no real benefit to getting them done at the same time. Although it’s possibly a good idea to get an electrician to check for loose connections at the input to the consumer unit after the meter “tails” have been moved around when installing a new meter.
Based on what I did over the last 18 months in the same situation I’d recommend:
- Get an electrician to take a look at your existing installation. When was the last EICR completed, if you have one at all? An EICR will need to be done before the consumer unit is changed, in any case. Make sure you get a proper electrician, not one of these cowboys that have done a 5 day course and now call themselves an electrician. A proper EICR will take the best part of a day for a typical property and involves disconnecting and testing every circuit in your consumer unit. If someone says they can get you an EICR certificate in an hour, walk away! Those cowboys are only for estate agents and landlords that just want a cheap certificate without caring about actual safety.
- The EICR will identify any existing problems with your installation. For the age, you most likely need uprated bonding and have “tails” that are too small in diameter, and these will need to be upgraded to 25mm^2 conductors. You’ll also need a double-pole isolator fitted to make it easier for your electrician to work on your installation. Both of these things can/will be done for free at the time of your smart meter installation. You might have to specifically ask for the isolator to be fitted.
- Once the meter is changed and all the supplier-side work is done, get your electrician back in to do the work on your side of the installation.