I am an owner of a firm of accountants (probably in a very different location though as our qualified starting rates are much lower!) and you are not being unreasonable.
What is your hourly charge out rate compared to the new starters?
Either their starting rates are too high when compared with the market or they're placing too much "value" on their flexibility for your pay. Have they struggled to recruit new starters in the past? Is there an indication that they only got these staff because they're willing to pay more?
Presumably you're working the same number of hours as they are?
If going rate is really about £68-79k for your position you could probably get a 4 day a week part time role with another firm for more money than you're currently paid!
Speak with a recruiter and see what they would say about your role. Use this as ammunition to go back to your employer.
"Following on from our recent conversation, it has come to my attention that newly qualified starters are earning only £1.5k a year less than what I'm earning. You mentioned before that my pay reflects some additional flexibility in my position, but I ultimately still work the same hours, at a higher level, than new starters and I don't think the ability to work from home occasionally [or whatever the flexibility is] should have that big a difference in my pay.
I have researched the market and the going rate for my level of experience is up to £78k per year. I do not expect to earn that much here, given the accommodations I have around family life, but I would appreciate the ability to renegotiate my contract."
You're not then specifically saying "or else I'll find somewhere else", but it is implied.
Their response will indicate how much they want you to stay.
When I handed my notice in at my previous firm, they came back the same day, offered me a new salary and a new location to try and convince me to stay.
I have a member of my team that isn't great at their job and if they came to me and asked for a pay increase, I might hold my ground (as, in their case, they definitely don't deserve any more) and if they choose to move on, so be it.