Orona and Synergy Housing appeared at Bournemouth Crown Court today (23 August) charged in connection with the incident.
Charges against a third company, Aster Property, also under s 3(1) of the act, have been ordered to lie on file.
On 13 August 2015 Alexys Brown got into the platform lift and put her head through a damaged vision panel. As the lift ascended to the first floor, her head became caught between part of the lift and the ground floor ceiling.
She died at the scene from head and neck injuries.
According to media reports, the companies were responsible for installing and servicing the lift, which had been fitted for Alexys' brother who uses a wheelchair.
Orona and Synergy Housing are due to be sentenced at Bournemouth Crown Court on 14-15 January 2019.
A HSE spokesperson said: "The HSE acknowledges today's guilty pleas but will not make a further comment until after sentencing."