We present a study of diffuse extended ionised gas toward three clouds located in the Galactic Centre (GC). One line of sight (LOS) is toward the 20 km s$^{-1}$ cloud (LOS$-$0.11) in the Sgr A region, another LOS is toward the 50 km s$^{-1}$ cloud (LOS$-$0.02), also in Sgr A, while the third is toward the Sgr B2 cloud (LOS+0.693). The emission from the ionised gas is detected from H$nalpha$ and H$mbeta$ radio recombination lines (RRLs). He$nalpha$ and He$mbeta$ RRL emission is detected with the same $n$ and $m$ as those from the hydrogen RRLs only toward LOS+0.693. RRLs probe gas with positive and negative velocities toward the two Sgr A sources. The H$mbeta$ to H$nalpha$ ratios reveal that the ionised gas is emitted under local thermodynamic equilibrium conditions in these regions. We find a He to H mass fraction of 0.29$pm$0.01 consistent with the typical GC value, supporting the idea that massive stars have increased the He abundance compared to its primordial value. Physical properties are derived for the studied sources. We propose that the negative velocity component of both Sgr A sources is part of gas streams considered previously to model the GC cloud kinematics. Associated massive stars with what are presumably the closest HII regions to LOS$-$0.11 (positive velocity gas), LOS$-$0.02 and LOS+0.693 could be the main sources of UV photons ionising the gas. The negative velocity components of both Sgr A sources might be ionised by the same massive stars, but only if they are in the same gas stream.
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